## anonymous one year ago 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

1. mathstudent55

We need to write it out with numbers.

2. mathstudent55

$$5 \sqrt 7 + 12 \sqrt 6 - 10 \sqrt 7 - 5 \sqrt 6$$

3. mathstudent55

Is that it?

4. anonymous

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

5. anonymous

Yes

6. mathstudent55

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?

7. mathstudent55

Now we combine like terms $$=-5\sqrt{7} + 7\sqrt{6}$$

8. mathstudent55

You can also leave it as $$=7\sqrt 6 - 5 \sqrt 7$$ Both answers are equivalent and correct.

9. anonymous

Thank you

10. mathstudent55

You're welcome.