What is square root and cube root?

Square root:

A square root of a number is a value that, when multiplied by itself, gives the number.

Square root of a number $x$ is a number $y$ such that $y.(y) = x$; in other words, a number $y$ whose square (the result of multiplying the number by itself, or $y ⋅ y$) is $x$.

For example, $5 \times 5 = 25$.

So, square root of 25 is 5.

Steps to find Square root by Prime Factorisation method:

Step I: Obtain the given number.

Step II: Resolve the given number into prime factors by successive division.

Step III: Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.

Step IV: Take one factor from each pair.

Step V: Find the product of factors obtained in step IV.

Step VI: The product obtained in step V is the required square root.

For example,

$7056=2\times2\times2\times2\times3\times3\times7\times7$

$7056=(2\times2)\times(2\times2)\times(3\times3)\times(7\times7)$

$7056=2^2\times2^2\times3^2\times7^2$

$7056=(2\times2\times3\times7)^2$

$7056=84^2$

Therefore, square root of 7056 is 84.

Cube root:

The cube root of a number is the value that when cubed gives the original number. Cube root of a number can be found by prime factorization and repeated estimation method without using factorization. There is also an advanced division method of finding cube roots of a  number.

For example,

Cube root of 216 is

$216 = 2 \times2 \times 2 \times 3 \times 3 \times 3 = (2\times3)^3 = (6)^3$ 

Cube root of 216 is 6.