[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
$=\sqrt{(248+\sqrt{64})}$
$=\sqrt{(248+8)}$
$=\sqrt{256}$
$=16$