Question

What is the least number that must be added to 2000 to make it a perfect square?

Answer 1

prime factors = (2*2)*(2*2)*(5*5)*5=2000  

2*2*2*2*5*5*(5*5) will be a perfect square

 

add 25 to 2000 = 2025

..

sqrt 2025 = 45

Answer 2

Concept-

Perfect square is the number from a given number system that can be expressed as a square of a number from the same number system.

Given-

The number is listed as 2000.

Find-

Find the smallest number that needs to be added to 2000 to make it a perfect square.

Solution-

"A perfect square is a number that can be expressed as the product of two equal integers." (What is a perfect square? A perfect square)

The first thing we notice is that it has to be an even digit because it ends with 00 ( 102=100,103=1,000 )

We further note that 16<20<25, as 16=42 and 25=52, 402<2000<502

Now 2000 is more or less in the middle between 1600 and 2500, two perfect squares.

We see that

452=40∗50+25=2025442=1936

So the smallest perfect square greater than 2000 is 2025

Therefore we need to add 2025-2000=25 to 2000 to get a perfect square

So 25 must be added to 2000 to make it a perfect square.

#SPJ2