How do you find the square root of 2000 in radical form?

We have to find the square root of 2000

Solution

To find the square root of 2000 we will factorise it first

Prime factorisation of 2000

Here we have to find the prime factors of 2000.

Divide 2000 by 2;

2000 ÷ 2 = 1000

Divide 1000 by 2

1000÷ 2 = 500

Divide 500 by 2

500 ÷ 2 = 250

Divide 250 by 2

250 ÷ 2 = 150

Divide 150 by 2

150 ÷ 2 = 75

Divide 75 by 3

75 ÷ 3 = 25

Divide 25 by 5

25 ÷ 5 = 5

Divide 5 by 5

5 ÷ 5= 1

By prime factorisation method, we will get,

2000 = 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5

√2000=√(2 × 2 × 2 × 2 × 3 × 2 × 5 × 5)

On paring

√2000=√{(2 x 2) (2x 2) x 3 x 2 x (5x 5)

√2000=√(2 x 2 x 5) (3 x 2)

√2000=20√6

Answer

Hence The square root of 2000 is 20√6

Hence, √2000 = 20√6

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