Question

Solve the problems:

1) Find the least number by which 8624 must be multiplied so that the product is a perfect square. Also find the square root of the perfect square.

2) Find the least number, that must be subtracted from 16142 to obtain a perfect square. Also, find the square root of the perfect square.

Please do it on a rough copy and send. I will mark your answer as branliest. ​

Answer 1

GivEn:

• Number = 8624

To find:

• The least number it must be multiplied.

Solution:

⌬ Let's do prime factorisation of the given number.

The prime factors are,

⇏ 2 × 2 × 2 × 2 × 7 × 7 × 11

The pairs are,

⇏ ( 2 × 2 ) × ( 2 × 2 ) × ( 7 × 7 ) × 11

[ Refer attachment ]

We see that,

⇏ 11 is unpaired.

∴ Hence, 8624 must be multiplied with 11 to obtain a perfect square.

Therefore,

⇏8624 × 11

⇏√94864

⇏308

∴ The square root of the perfect square is 308.

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⇏ Question 2

Given number, 16142.

We are asked to find,

• The number it must be subtracted to get a perfect square.

⌬ Let's do long division method.

The remainder is,

[ Refer attachment ]

⇏ 13

⇏ 16142 - 13

⇏ 16129

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« Now, Let's find Square root of it,

⇏ √16129

⇏ 127

∴ Hence, 13 must be subtracted from 16129 to obtain a perfect square number.