Emer says she has worked out that 3-√5 is a square root of 14-6√5. Showing all your work out clearly. prove that Emer is correct.
Simplify the following:
sqrt(14 - 6 sqrt(5))
Factor 2 out of 14 - 6 sqrt(5) giving 2 (7 - 3 sqrt(5)):
sqrt(2 (7 - 3 sqrt(5)) )
2 (7 - 3 sqrt(5)) = 9 - 6 sqrt(5) + 5 = 9 - 6 sqrt(5) + (sqrt(5))^2 = (3 - sqrt(5))^2:
sqrt((3 - sqrt(5))^2 )
Cancel exponents. sqrt((3 - sqrt(5))^2) = 3 - sqrt(5):
Answer: |3 - sqrt(5)
