SQUARE ROOT AND CUBE ROOT| CUET L-5

Square Root And Cube Root

 

Square root and Cube roots are the most important topics in Maths, especially for class 8 students. To find the square root of any number, we need to find a number which when multiplied twice by itself gives the original number. Similarly, to find the cube root of any number we need to find a number which when multiplied three times by itself gives the original number.

 

Symbol: The square root is denoted by the symbol ‘√’, whereas the cube root is denoted by ‘∛’.

 

Examples:

 

√4 = √(2 × 2) = 2

 ∛27 = ∛(3 × 3 × 3) = 3

Square Root and Cube Root Table

Memorizing the squares and the square roots of the first few numbers are almost elementary and it can help you to solve problems much faster rather than having to work on it. Following is the square roots list and Cube root list of the first 15 natural numbers.

 

Number Square root (√) Cube root (∛)

1 1.000 1.000

2 1.414 1.260

3 1.732 1.442

4 2.000 1.587

5 2.236 1.710

6 2.449 1.817

7 2.646 1.913

8 2.828 2.000

9 3.000 2.080

10 3.162 2.154

11 3.317 2.224

12 3.464 2.289

13 3.606 2.351

14 3.742 2.410

15 3.873 2.466

 

How to find Square Root and Cube Root

To find the square root of the number, we have to determine which number was squared to get the original number. For example, if we have to find the root of 16, then as we know, when we multiply 4 by 4, the result is 16. Hence, √16 = 4. Similarly, if we have to find the cube root of a number, say 64, then it is easy to determine that the cube of 4 gives 64. So the cube root of 64 is 4. But if the numbers are very large, then to find the roots, we have to use the prime factorisation method. Let us see some examples.

 

Solved Examples

Example 1: Find Square root of 256.

 

Solution: Given: The number is 256.

 

Prime factorisation of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = (2 × 2 × 2 × 2)2 = 16^2

 

Taking roots on both the sides, we get;

 

√256 = 16.

 

Hence, 16 is the answer.

 

Example 2: Find the cube root of 512.

 

Solution:

 

Given: The number is 512.

 

Prime factorisation of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = (2 × 2 × 2)3 = 8^3

 

Taking the cube root on both the sides we get;

 

∛512 = 8

 

Hence, 8 is the answer.