Question

Between which pair of consecutive integers does √111 lie

A: 20 and 22
B: 10 and 11
C: 4 and 5
D: 5 and 6

Answer 1

B. 10 and 11
This is because 10x10 is 100, so thats less than what you need and then 11x11 is 121, and that is more than you need... So it would be between 10 and 11.

Answer 2

The given lie between 10 and 11

B is correct

Explanation:

We need to find pair of number in which
`√(111)` lie between them.

Let given number lie between two integer x and y

Thus,

`x<√(111)<y`

Taking square both sides

`x^2<111<y^2`

As we assumed x and y are integers.

We will choose two number across 111 those are perfect square.

`100<111<121`

`10^2<111<11^2`

Taking square root all sides

`10<√(111)<11`

Hence, The given lie between 10 and 11.