Asked by nishika
evaluate sqrt(5+2*(sqrt6)) + sqrt(8-2*(sqrt15))
Answers
Answered by
Graham
Use: √(a+2√(ab)+b) = √a + √b
Too: √(a-2√(ab)+b) = √a - √b
√(5+2√6) + √(8-2√15)
= √(2+2√2√3+3) + √(8-2√15)
= √((√2+√3)^2) + √(8-2√15)
= √2 + √3 + √(8-2√15)
= √2 + √3 + √(5-2√3√5+3)
= √2 + √3 + √((√5-√3)^2)
= √2 + √3 + √5 - √3
= √2 + √5
Too: √(a-2√(ab)+b) = √a - √b
√(5+2√6) + √(8-2√15)
= √(2+2√2√3+3) + √(8-2√15)
= √((√2+√3)^2) + √(8-2√15)
= √2 + √3 + √(8-2√15)
= √2 + √3 + √(5-2√3√5+3)
= √2 + √3 + √((√5-√3)^2)
= √2 + √3 + √5 - √3
= √2 + √5
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.