anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
We need to write it out with numbers.
mathstudent55
  • mathstudent55
\(5 \sqrt 7 + 12 \sqrt 6 - 10 \sqrt 7 - 5 \sqrt 6\)
mathstudent55
  • mathstudent55
Is that it?

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anonymous
  • anonymous
\[5\sqrt{7} + 12\sqrt{6} - 10\sqrt{7} - 5\sqrt{6}
anonymous
  • anonymous
Yes
mathstudent55
  • 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?
mathstudent55
  • mathstudent55
Now we combine like terms \(=-5\sqrt{7} + 7\sqrt{6}\)
mathstudent55
  • mathstudent55
You can also leave it as \(=7\sqrt 6 - 5 \sqrt 7\) Both answers are equivalent and correct.
anonymous
  • anonymous
Thank you
mathstudent55
  • mathstudent55
You're welcome.

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