Question

I Need Help PLease!

Ashton estimates the square root of 72 in the following way:
√72=
2√36=
2×6=12
Explain why his reasoning is incorrect.
Estimate the square root of 72 to the nearest tenth without using your calculator. Show your work.
Answer:

Answer 1

Hello!

The answer is: The square root of 72 is 8.5

Why?

To solve this problem we need to remember how to operate with square roots.

$\sqrt{a*b}=\sqrt{a}*\sqrt{b}$

So, we are asked to estimate the square root of 72, to find the problem, we need to factor 72, and then, apply the square root property.

$\sqrt{72}=\sqrt{2*36}$

Now, since 36 is a perfect square (it can be obtained by squaring a whole number), we have:

$\sqrt{72}=\sqrt{2*36}=\sqrt{2}*\sqrt{36}=\sqrt{2}*6=8.48$

Then, we have that 8.48 rounded to the nearest tenth is equal to 8.5.

Hence, we have that , the square root of 72 is equal to 8.5.

Have a nice day!