Question

please answer by solving
by what smallest number by which 1152 must be multiplied so that it becomes a perfect square also find the number whose square is the new number ​

Answer 1

Answer:

For a number to be a perfect square, each prime factor has to be paired. Hence, 1152 must be divided by 2 for it to be a perfect square.

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Answer 2

Step-by-step explanation:

Given :-

The number = 1152

To find:-

By what smallest number by which 1152 must be multiplied so that it becomes a perfect square also find the number whose square is the new number ?

Solution :-

Given number = 1152

It can be written as

1152 = 2×576

1152 = 2×2×288

1152 = 2×2×2×144

1152 = 2×2×2×2×72

1152 = 2×2×2×2×2×36

1152 = 2×2×2×2×2×2×18

1152 = 2×2×2×2×2×2×2×9

1152 = 2×2×2×2×2×2×2×3×3

It can be arranged as

1152 = (2×2)×(2×2)×(2×2)×2×(3×3)

Clearly 1152 is not a perfect square number.

So, if we multiply 1152 with 2 then the result will be a perfect square number.

1152 × 2 = 2304

2304 = 1152 × 2

2304 = (2×2)×(2×2)×(2×2)×(2×2)×(3×3)

Square root of 2304 = √2304

=>√[(2×2)×(2×2)×(2×2)×(2×2)×(3×3)]

=> 2×2×2×2×3

=> 48

Therefore,√2304 = 48

Answer:-

The required number must be multiplied by 1152 is 2

The square root of the resultant number is 48

Used Method:-

• Prime Factorization method