Let’s do this by examples

 

Question

Finds the smallest number divided to 32 to get a perfect square.

26.jpg

 

Since 2 does not occur in pairs,

we divide by 2 to make it a pair

 

So, our number becomes

  32 × 1/2 = 2 × 2 × 2 × 2 × 2 × 1/2

Smallest number divided to get perfect square - Part 2

 

Now, it becomes a perfect square.

 

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

 

Question

Finds the smallest number divided to 90 to get a perfect square.

Smallest number divided to get perfect square - Part 3

Here,

2 & 5 do not occur in pairs

So, we divide by 2 and 5 to make pairs

 

So, our number becomes

   90 × 1/2 × 1/ 5 = 2 × 3 × 3 × 5 × 1/2 × 1/5

Smallest number divided to get perfect square - Part 4

 

Now, it becomes a perfect square.

 

So, we divide 90 by 2 × 5

i.e. 10  to make it a perfect square

 

Question

Finds the smallest number divided to 120 to get a perfect square.

Smallest number divided to get perfect square - Part 5

 

Here,

2, 3 & 5 do not occur in pairs

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

 

So, our number becomes

Smallest number divided to get perfect square - Part 6

 

Now, it becomes a perfect square.

 

So, we divide 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.