How do you find the square root of 576?

Method-I Using Prime Factorisation

Prime factorisation of 576 is

So, 576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

By pairing the prime factors, we get

576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

So, we have

567 = 2 x 2 x 2 x 3

=24

Method-II Using Long Division

Make a pair of digits of a given number starting with a digit at one's place. Put a bar on each pair.

Now we have to multiply a number by itself such that the product ≤ 5.

Here 2 x 2 = 4 ≤ 5, so divisor is 2 and quotient is 2. Now do the division and get the remainder.

Now, we have to bring down 76 and quotient 2 is multiplied by 2 becomes 4, which is starting digit of new divisor

4 should be the digit at one's place of new divisor because when 44 is multiplied by 4 we get 176.

So new divisor is 44 and next digit of quotient is 4. Now do the division and get the remainder.

Hence, the square root of 576 is 24.

By using the prime factorisation and the long division method we can find the square root of 576 is 24.