Question

Find two consecutive whole numbers between which `sqrt71` lies.?

Answer 1

The two numbers are `8` and `9`.

Explanation:

To figure this out, first, I would list a few numbers and their radical equivalents. I'll start from `6`:

#color(white){color(black)( (6, qquadsqrt36), (7, qquadsqrt49), (8, qquadsqrt64), (9, qquadsqrt81), (10, qquadsqrt100)):}#

Now, we have to find the two radicals that are consecutive where one of them is bigger than `sqrt71` and the other is smaller.

These two numbers are `sqrt64` and `sqrt81` (because `64<=71<=81`). That means that the two whole numbers are `8` and `9`.

You can verify this by using a calculator to compute `sqrt71`:

`sqrt71~~8.42614...`

This number is between `8` and `9`, so our answer is correct.

Answer 2

`8` and `9`

Explanation:

To find two consecutive whole numbers that `sqrt71` lies between, we must first find two square roots that a) are consecutive perfect squares (are the squares of whole numbers) and b) `sqrt(71)` lies between.

Let's write out some perfect squares:

`1^2=1`
`2^2=4`
`3^2=9`
`4^2=16`
`5^2=25`
`6^2=36`
`7^2=49`
`8^2=64`
`9^2=81`

From the above, we see that `sqrt(64)` and `sqrt(81)` meet our above conditions: they are consecutive perfect squares and `sqrt(71)` lies between them.

So, `sqrt(71)` lies between `sqrt(64)=8` and `sqrt(81)=9`