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

Answer:

$\sqrt {72} = 6\sqrt 2$

Step-by-step explanation:

Ashton estimates the square root of 72 in the following way:

√72=

2√36=

2×6=12

a) Explain why his reasoning is incorrect

This is incorrect because $\sqrt2 * 6$ is the correct answer but he has missed the square root term on 2.

$=\sqrt {2^2X2X3^2 }$

$=\sqrt {2^2} \sqrt 2 \sqrt {3^2 }$

$=2 X \sqrt 2 X 3$

$= \sqrt 2 X 6$

or can be written as:

$= 6\sqrt 2$

b) Estimate the square root of 72 to the nearest tenth without using your calculator. Show your work.

Find the factors of 72 we get $\sqrt {2X2X2X3X3 }$  

Now, we will combine 2 terms if the are same so,

$=\sqrt {2^2X2X3^2 }$

$=\sqrt {2^2} \sqrt 2 \sqrt {3^2 }$

$=2 X \sqrt 2 X 3$

$= \sqrt 2 X 6$

$= 6\sqrt 2$

$\sqrt {72} = 6\sqrt 2$