Question

1458 - By which smallest number this number should be multiplied, so that the result becomes a perfect square? Find the square root of the result obtained.

Answer 1

Hey Mate !!


The prime Factorization of 1458 is,

1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3


Here, We can see the number 3 is paired 3 times while 2 is remained unpaired.

When we multiply 1458 with 2. The product is 1458 × 2 = 2916

The prime Factorization of 2916 is

2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

All numbers are paired. Hence, 2916 is a perfect square. The Square root is :

= 2 × 3 × 3 × 3

= 18 × 3

= 54

Therefore,

The Square root of 2916 is 54

Answer 2

Solution :

Resolving 1458 into prime factors,

1458 = 2×2×2×2×7×13

= (2×2)×(2×2)×7×13

We can see 2,2 exists in pairs,

While 7 , 13 do not exists in

pairs .

So , we must multiply the given

number by 7 × 13 = 91 to get

a perfect square .

Therefore ,

the perfect square so obtained

is 1458 × 91 = 132678

Square root of 132678

√132678

= √(2×2)(2×2)(7×7)(13×13)

= 2×2×7×13

= 364

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