Question

Find the least number by which 21160 should be divided to make it a perfect square​

Answer 1

Answer:

10

Step-by-step explanation:

21160 is not a perfect square. In that case, let us factorise it to find the number to be divided

21160 = 2 × 2 × 2 × 5 × 23 × 23

=>21160 = 2³ × 5 × 23² = 2² × 2 × 5 × 23² = 2² × 10 × 23²

Since 10 is the only number among the factors without any pair, we get our answer as 10.

To prove our answer, let us divide 21160 by 10 and check.

21160 ÷ 10 = 2116

On factorising 2116,

2116 = 2² × 23²

=> $\sqrt{2116} =$  2 × 23 = 46

Since square root of 2116 is a rational number, it is a perfect square.

Hence, we can confirm that the smallest no. by which 21160 should be divided to get a perfect square is 10.

PLEASE MARK BRAINLIEST

Answer 2

Answer:

10

Step-by-step explanation:

21160 is not a perfect square. In that case, let us factorise it to find the number to be divided

21160 = 2 × 2 × 2 × 5 × 23 × 23

=>21160 = 2³ × 5 × 23² = 2² × 2 × 5 × 23² = 2² × 10 × 23²

Since 10 is the only number among the factors without any pair, we get our answer as 10.

To prove our answer, let us divide 21160 by 10 and check.

21160 ÷ 10 = 2116

On factorising 2116,

2116 = 2² × 23²

=>   2 × 23 = 46

Since square root of 2116 is a rational number, it is a perfect square.

Hence, we can confirm that the smallest no. by which 21160 should be divided to get a perfect square is 10.

PLEASE MARK BRAINLIEST