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
