[latexpage]

**Square root**

If you have to find square of a number then we write

$x^2=y$

it means we multiplied x two times and got y.

For example find the square of 2 that you have to multiple 2 two times

$2^2=2*2=4$

We find square of a number by multiplying that number twice.

So what is a square root

Finding a square root is reverse process of square.

In square root we find the number which is multiplied itself to get the square of number.

a square root is represented by symbol

$\sqrt{x}$

This symbol is known as square root.

here x represents the number whose square root we want to find

In general

if $x^2=y$ then

$\sqrt{y}=\sqrt{x*x}=x$,

$\sqrt{4}=\sqrt{2*2}=2$

$\sqrt{9}=\squr{3*3}=3$

in above example

Square root of y is x

square root of 4 is 2

square root of 9 is 3

Example find the value of $\sqrt{36}$

We all know 36 is square of 6

so we can write $\sqrt{6*6}$

so $\sqrt{36}$=$\sqrt{6*6}=6$

Find the $\sqrt{81}$

$\sqrt{81}=$\sqrt{9*9}=9

Finde the square root of 625

by factoring 625

we get 625=5*5*5*5

so $\sqrt{625}$

=$\sqrt{5*5*5*5}$

=5*5

=25

To find the square root of 2 is as below

**Cube root**

We can find cube of a number by multiplying it three times

for example to find cube root of x we multiply it tree times

$x^3=x*x*x=y$

Here y is cube of x

Finding the cube of 2

that is

$2^3=2*2*2=8$

here 8 is cube of 2

similar

$3^3=3*3*3=27$

$4^3=4*4*4=64$

Now what is cube root

Cube root is a reverse process of a cube.

In cube root we find the number which is multiplied itself thrice to get the cube of number.

$\sqrt[3]{x}=y$ here $\sqrt[3]{x}$ is known as cube root of $x=y$

Cube root is represented by $\sqrt[3]{x}$

$\sqrt[3]{8}=\sqrt{(2*2*2)}=2$

$\sqrt[3]{x+y}$

here x is number whose cube root we want to fine

**Finding Square & cube root by factorization**

Find th square root of 6084

$\sqrt{6084}= \sqrt{2*2*3*3*13*13}=2*3*17=78$

Calculate the value of $\sqrt{(248+\sqrt{(51+\sqrt{169})})}$

$\sqrt{(248+\sqrt{(51+\sqrt{169})})}$

$=\sqrt{(248+\sqrt{(51+13)})}$ 169 is square of 13

$=\sqrt{(248+\sqrt{64})}$

$=\sqrt{(248+8)}$

$=\sqrt{256}$

$=16$