Question

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

Answer 1

Answer:

To show: $\sqrt{21}$ 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

$\sqrt{16} <\sqrt{21}<\sqrt{25}$

Simplify:

$4 < \sqrt{21} < 5$

⇒$\sqrt{21}$ lies between 4 and 5.

Therefore,  $\sqrt{21}$ is between $\sqrt{16}$ and $\sqrt{25}$ this means $\sqrt{21}$ lies between 4 and 5.

Answer 2

Answer:

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

$\sqrt{16} < \sqrt{21}<\sqrt{25}$

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

$4<\sqrt{21}<5$, because $\sqrt{16}=4$ and $\sqrt{25}=5$

So, basically, the reason why $\sqrt{21}$ 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.