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

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

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`