Question

How many non perfect squares are there between 9 Square and 10 square .Formula for this question

Answer 1

Solution :

Number of non square Numbers

between 9² and 10²

= 2 × base of the first Number

= 2 × 9

= 18

•••••

Answer 2

Okay first find $9^2$ and $10^2$

$9^2=81$

$10^2=100$

Number of non - perfect squares = 100-81-1

==)18

We know that 18=9*2

This means that if:

x and y are consecutive perfect squares:

such that x+1=y

then:

number of non-perfect squares between them is x*2

or 2x

Proof:

$y^2-x^2-1$   is the number of non-pefect square

$\implies (x+1)^2-x^2-1$

$\implies x^2+2x+1-x^2-1$

$\implies 2x$

Hence proved

Hope it helps you.