How do you find the square root of 500?

We have to find the square root of 500.

Solution

We will find the square root of 500 by using prime factorisation method

Prime factorisation of 500

Here we have to find the prime factors of 500

Divide 500 by 2

500÷2 = 250

Divide 250 by 2

250 ÷ 2 = 125

Divide 125 by 5;

125 ÷ 5 = 25

Divide 25 by 5

25 ÷ 5 = 5

Divide 5 by 5

5 ÷ 5 = 1

Now, we have got the quotient as 1. So no further division is possible.

Therefore, the prime factorisation of 500 is 2 x 5 × 5 × 5

On pairing we get

500 = 2 x 2 x 5 × (5 × 5 )

√500 =√ ( 5 x 5) ( 2 x 2) x 5

√500 = 10√5

Substituting the √5 value we get

√500 = 10 X 2.236

√500 = 22.3606

Answer

The square root of 500 = 22.3606

√500 = 22.3606

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