Question

In: Advanced Math

Number Theory 1

What is the quickest way to determine if a number is a perfect square?

Solutions

Expert Solution

After brainstorming for hours and visiting websites and blogs on Mathematics I finally came to the conclusion that there are not any tricks available to check if a given number is a perfect square.

 

But there is a check if a given number is not a perfect square, you just have to apply the following 2 steps,

 

1.A Perfect Square always ends with one of these numbers ( 0, 1, 4, 5, 6, 9). If it doesn’t, given number is not a Perfect Square.

 

2. Now if it satisfies above condition then check the digital summation of a number. In digital summation you keep on adding all the digits of a number till you get a single number.

A Perfect Square always have digital summation of one of these numbers ( 1, 4, 7, 9), if it doesn’t it’s not a Perfect Square.

 

Example :

 

1.263 : Ends with 3, not a perfect square.

 

2. 371 : Ends with 1, so it might be a perfect square. Go to step 2.

Digital Summation : 3+7+1 = 11 = 1+1 = 2. So, not a Perfect Square.

A Perfect Square always have digital summation of one of these numbers ( 1, 4, 7, 9), if it doesn’t it’s not a Perfect Square.

Nipun Maity answered 2 years ago
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