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

  1. Chapter 6 Class 8 Squares and Square Roots
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.