Question

Use the drop-down menus to complete each statement to show why √21 is between 4 and 5.

Answer 1

We know that

`16<21<25`

Because, 16 is less than 21 and 25 is more than 21.

Now, if we apply a square root to each part, we would have

`√(16) < √(21)<√(25)`

Then, we solve each square root, except the square root of 21, because it doesn't have an exact result

`4<√(21)<5`, because
`√(16)=4` and
`√(25)=5`

So, basically, the reason why
`√(21)` is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.

Answer 2

To show:
`√(21)` is between 4 and 5

We know:

21 is lies between two consecutive integer i.e, 16 and 25

We can write this as:

`16 < 21 < 25`

or

`√(16) <√(21)<√(25)`

Simplify:

`4 < √(21) < 5`

⇒
`√(21)` lies between 4 and 5.

Therefore,
`√(21)` is between
`√(16)` and
`√(25)` this means
`√(21)` lies between 4 and 5.