The square root of a number is the value that multiplied by itself gives the original number. If m is the square root of n, then it is represented as m = √n. Also, we can write this expression as m² = n. √ is the root of numbers. The square root of the square of a positive number gives the original number. For example, the square of 4 is 16, 4² = 16, and the square root of 16, √16 = 4. Let us say n is a positive integer, such that √(n . n) = √(n²) = n.
The square root of a negative number represents a complex number. √-m = mi, where i is the imaginary number.
Quick Links of Square Root Concepts
Below is the list of several concepts available in the Square Roots Chapter. You can get a grip on them by simply tapping on the direct links available. You just need to tap on them and learn the concept individually. Practice the Problems on finding Square Root of Numbers in Decimal Form, Fraction Form, etc.
- Square Root of a Perfect Square by using the Prime Factorization Method
- Square Root of a Perfect Square by Using the Long Division Method
- Square Root of Numbers in the Decimal Form
- Square Root of Number in the Fraction Form
- Square Root of Numbers that are Not Perfect Squares
- Table of Square Roots
- Practice Test on Square and Square Roots
How to Find the Square Root?
The square root of any number can be easily found for a given number using the given method. If the given number is a perfect square, then we can find the factors by the prime factorization method. If the number is an imperfect square, then we can use the long division method to find the root.
Example: Square of 8 = 8 x 8 = 8² = 64
The square root of 64, √64 = 8.
Square Root Examples
(i) 1² = 1
Therefore, the square root of 1 is 1. Also, it can write as √1 = 1.
(ii) 2² = 4
Therefore, the square root of 4 is 2. Also, it can write as √4 = 2.
(iii) 3² = 9
Therefore, the square root of 9 is 3. Also, it can write as √9 = 3.
(iv) 5² = 25
Therefore, the square root of 25 is 5. Also, it can write as √25 = 5.
(v) 4/3 is the square root of 16/9. Since 4²/3² = 4/3
Or we can write it as √(16/9) = 4/3 (Square root of 16/9 is 4/3)
(vi) 0.3 is the square root of 0.09. Since 0.3² = 0.09
Or we can write it as √0.09 = 0.3 (Square root of 0.09 is 0.3)
In general; if n = m², then m is the square root of n, i.e., m = √n
How to Solve the Square Root Equation?
The square root equations are solved using the below steps. Square both the sides of the given equation then simplify it to find the answer.
Example: Solve √(9a + 4) – 5 = 0
Solution: Given, √(9a + 4) – 5 = 0
Isolate the square root term first. Then the equation becomes, √(9a + 4) = 5
Now on squaring both the sides, we get; 36a + 16 = 25
36a + 16 = 25
36a = 25 – 16
a = 9/36
a = 1/4