Question

Simplify 5 square root of 7 end root plus 12 square root of 6 end root minus 10 square root of 7 end root minus 5 square root of 6.

A.5 square root of 14 end root minus 7 square root of 12

B. 5 square root of 7 end root minus 7 square root of 6

C. 7 square root of 12 end root minus 5 square root of 14

D. 7 square root of 6 end root minus 5 square root of 7

Answer 1

We need to write it out with numbers.

Answer 2

\(5 \sqrt 7 + 12 \sqrt 6 - 10 \sqrt 7 - 5 \sqrt 6\)

Answer 3

Is that it?

Answer 4

\[5\sqrt{7} + 12\sqrt{6} - 10\sqrt{7} - 5\sqrt{6}

Answer 5

Yes

Answer 6

Ok. Terms that have the same root are like terms and can be combined.
There are two terms with \(\sqrt 6\) and two terms with \(\sqrt 7\).
We can change the order of the operations and group the like terms together.

\(5\sqrt{7} + 12\sqrt{6} - 10\sqrt{7} - 5\sqrt{6} \)

\(=5\sqrt{7} - 10\sqrt{7} + 12\sqrt{6} - 5\sqrt{6} \)

Ok?

Answer 7

Now we combine like terms

\(=-5\sqrt{7} + 7\sqrt{6}\)

Answer 8

You can also leave it as

\(=7\sqrt 6 - 5 \sqrt 7\)

Both answers are equivalent and correct.

Answer 9

Thank you

Answer 10

You're welcome.