Question

8. How many non-square numbers lie between
() 90and 91
(1) 1,000 and 1,001
(Hint: There are 2n square numbers between n' and (n+1)".​

Answer 1

1) ANSWER = The following pair of numbers 90² and 91².

Here, n =90

We need to find the non square number lies between them.

Since we know that ,

Number of non square numbers is given by

2n=2\times 90=1802n=2×90=180

Hence, there are 180 non square numbers lie between 90 and 91.

2) ANSWER =

{1001}^{2} - {1000}^{2}1001

2

−1000

2

to do this in a simple method, we will have to use the identity.

{a}^{2} - {b}^{2}a

2

−b

2

which is

( a + b ) ( a - b )

a is 1001 , b is 1000

let us substitute...

we get,

( 1001 + 1000 )( 1001 - 1000 )

which is ,

2001 ( 1)

=> 2001...

so, there are 2000 numbers between these two squares...

as the 2001 numbers might include one of the two numbers, 1000 or 1001, soo.. 2001-1

hope it helps!