Question

what is the least positive integer n by which 99 should be multiplied so that 99× n is a perfect square

Answer 1

99 = 3 x 3x 11

therefore for perfect square we should multiply it by 11

ans n= 11

Answer 2

The value of n = 11

Given:

99 × n

To find:

The value of n so that 99 × n be a perfect square

Solution:

A perfect square:

• A perfect square is a number which is obtained multiplying same number 2 times. For example: 4 = 2×2, 9 = 3×3 .... etc
• Square numbers can written in the form of a²

Here, given number 99 × n

To find the n value write 99×n as product of its prime factors

= 3 × 3 × 11 × n  

Now group the factors as squares

3 × 3 × 11 × n  = 3² × 11 × n  

Here, 11 is left out

So to be a perfect square number 99 × n need another 11

Then n must be equals to 11

Therefore, the value of n = 11

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