Question

Find the largest 3 digit number which is a perfect square.

(I know the answer is 961. I want to know the method. There is probably a unique method to find the answer to this.)

Answer 1

Answer:

This is an example:

If u don't understand write in comment immediately....

Answer 2

Answer:

First you have to check the squares of certain numbers

For example,

$2 {}^{2} = 4 \\ 14 { }^{2} = 196 \\ 21 {}^{2} = 441 \\ 30 {}^{2} = 900$

As we know that 999 is the largest 3 digit number, here we got 30 square = 900

Then we have to check the squares of the numbers nearest to 30.

$31 {}^{2} = 961 \\ 32 {}^{2} = 1024$

After 31 square all squares are beyond 3 digit number.

Therefore the number 961 (31 square ) is the largest 3 digit perfect square number .