Question

What is the exact value of the expression the square root 72. − the square root of 8. + the square root of 128.? Simplify if possible.

8the square root of 2.
12the square root of 2.
8the square root of 3.
12the square root of 3.

Answer 1

\[\sqrt 72 - \sqrt 8 + \sqrt 128\]

Correct?

Answer 2

yup

Answer 3

\[\sqrt 72 = \sqrt 8 \times 9 = \sqrt 2 \times 2 \times 2 \times 3 \times 3 = 2 \times 3 \sqrt 2 = 6 \sqrt 2\]
\[\sqrt 8 = \sqrt 4 \times 2 = 2 \sqrt 2\]
\[\sqrt 128 = \sqrt 4 \times 32 = \sqrt 4 \times 4 \times 4 \times 2 = 8 \sqrt 2\]

Answer 4

Does that make sense to you?

Answer 5

yes

Answer 6

\[6 \sqrt 2 - 2 \sqrt 2 + 8 \sqrt 2 = 12 \sqrt 2\]

You basically only care about the number on the front. Since they are all multiplying by sqrt 2, you can treat them as like terms.

Answer 7

ohhhh!

Answer 8

thank you so much!