Let’s do this by examples

 

Finds the smallest number multiplied by 32 to get a perfect square.

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Since 2 does not occur in pair,

we multiply by 2 to make it a pair

 

So, our number becomes

Smallest number multiplied to get perfect square - Part 2

Now, it becomes a perfect square.

 

So, we multiply 32 by 2 to make it a perfect square

 

 

Finds the smallest number multiplied by 90 to get a perfect square.

Smallest number multiplied to get perfect square - Part 3

Here,

2 & 5 do not occur in pairs

So, we multiply by 2 and 5 to make pairs

 

So, our number becomes

   90 × 2 × 5 = 2 × 3 × 3 × 5 × 2 × 5

Smallest number multiplied to get perfect square - Part 4

Now, it becomes a perfect square.

 

So, we multiply 90 by 2 × 5

i.e. 10  to make it a perfect square

 

Finds the smallest number multiplied by 120 to get a perfect square.

Smallest number multiplied to get perfect square - Part 5

Here,

2, 3 & 5 do not occur in pairs

So, we multiply by 2, 3 and 5 to make pairs

 

So, our number becomes

     120 × 2 × 3 × 5 = 2 × 2 × 2 × 3 × 5 × 2 × 3 × 5

Smallest number multiplied to get perfect square - Part 6

Now, it becomes a perfect square.

 

So, we multiply 120 by 2 × 3 × 5

i.e. 30  to make it a perfect square

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.