Students can use the Spectrum Math Grade 8 Answer Key Chapter 2 Lesson 2.3 Cube Roots as a quick guide to resolve any of their doubts.
Spectrum Math Grade 8 Chapter 2 Lesson 2.3 Cube Roots Answers Key
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 27 is 3: = 3.
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Identify the cube root.
Question 1.
a.
= _____
Answer: 12
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 1728 is 12.
= 12
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= _____
Answer: 9
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 729 is 9.
= 9
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= _______
Answer: 35
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 42875 is 35.
= 35
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 2.
a.
= _______
Answer: 15
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 3375is 15.
= 15
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= _____
Answer: 8
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 512 is 8.
= 8
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= _____
Answer: 25
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 15625 is 25.
= 25
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 3.
a.
Answer: 20
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 8000 is 20.
= 20
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
Answer: 5
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 125 is 5.
= 5
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
Answer: 7
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 343 is 7.
= 7
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 4.
a.
= _____
Answer: 2
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 8 is 2.
= 2
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= _____
Answer: 4
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 64 is 4.
= 4
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= _____
Answer: 10
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 1000 is 10.
= 10
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 5.
a.
= ____
Answer: 3
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 27 is 3.
= 3
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= ____
Answer: 6
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 216 is 6.
= 6
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= ____
Answer: 40
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 64000 is 40.
= 40
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 6.
a.
= ____
Answer: 50
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 125000 is 50.
= 50
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= ____
Answer: 70
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 343000 is 70.
= 70
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= ____
Answer: 60
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 216000 is 60.
= 60
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 7.
a.
= ____
Answer: 1
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 1 is 1.
= 1
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= ____
Answer: 100
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 1000000 is 100.
= 100
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= ____
Answer: 30
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 27000 is 30.
= 30
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 8.
a.
= ____
Answer: 80
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 512000 is 80.
= 80
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
= ____
Answer: 90
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 729000 is 90.
= 90
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
c.
= ____
Answer: 200
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 8000000 is 200.
= 200
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Cube roots can be estimated by finding cube roots on either side of the desired root. is between 5 and 6 because
is 5 and
is 6. Therefore,
is between 5 and 6, but closer to 5 because 130 is closer to 125 than it is to 216.
Fractions can also have cube roots. For example, = \(\frac{1}{2}\) because \(\frac{1}{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{8}\)
Find the cube root of each number.
Question 1.
a.
Answer: \(\frac{1}{4}\)
Fractions can also have cube roots.
= \(\frac{1}{4}\)
because \(\frac{1}{4}\) × \(\frac{1}{4}\) × \(\frac{1}{4}\) = \(\frac{1}{64}\)
b.
Answer: \(\frac{2}{3}\)
Fractions can also have cube roots.
= \(\frac{2}{3}\)
because \(\frac{2}{3}\) × \(\frac{2}{3}\) × \(\frac{2}{3}\) = \(\frac{8}{27}\)
c.
Answer: 8
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 512 is 8.
= 8
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 2.
a.
Answer: 0
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 0 is 0.
= 0
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
b.
Answer: \(\frac{4}{5}\)
Fractions can also have cube roots.
= \(\frac{4}{5}\)
because \(\frac{4}{5}\) × \(\frac{4}{5}\) × \(\frac{4}{5}\) = \(\frac{64}{125}\)
c.
Answer: 1
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 1 is 1.
= 1
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 3.
a.
Answer: \(\frac{2}{6}\)
Fractions can also have cube roots.
= \(\frac{2}{6}\)
because \(\frac{2}{6}\) × \(\frac{2}{6}\) × \(\frac{2}{6}\) = \(\frac{8}{216}\)
b.
Answer: \(\frac{5}{7}\)
Fractions can also have cube roots.
= \(\frac{5}{7}\)
because \(\frac{5}{7}\) × \(\frac{5}{7}\) × \(\frac{5}{7}\) = \(\frac{125}{343}\)
c.
Answer: 4
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The cube root of 64 is 4.
= 4
The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Estimate the following cube roots.
Question 4.
is between ____ and ____ but closer to ____
Answer: is between 2 and 3 but closer to 2.
is between 2 and 3 but closer to 2, because 10 is closer to 8 than to 27.
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 5.
is between ____ and ____ but closer to ____
Answer: is between 4 and 5 but closer to 5.
is between 4 and 5 but closer to 5, because 110 is closer to 64 than to 125.
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 6.
is between ____ and ____ but closer to ____
Answer: is between 7 and 8 but closer to 8.
is between 7 and 8 but closer to 8, because 500 is closer to 343 than to 512.
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 7.
is between ____ and ____ but closer to ____
Answer: is between 5 and 6 but closer to 5.
is between 5 and 6 but closer to 5, because 155 is closer to 125 than to 216.
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.
Question 8.
is between ____ and ____ but closer to ____
Answer: is between 10 and 11 but closer to 11.
is between 10 and 11 but closer to 11, because 1322 is closer to 1331 than to 1000.
The cube of a number is that number multiplied by itself three times. A cube is expressed as n3, which means n × n × n or n cubed. The cube root of a number is the number that, multiplied by itself and by itself again, equals that number. The expression of a cube root is called a radical. The symbol is called a radical sign. The 3 on the radical sign shows that this is a cube root.