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How do you simplify #5/(8+sqrt(7))#?

Answer 1

Eva Abramson

#(40-5sqrt7)/57#

Original expression

#5/(8+sqrt7)#

Multiply by conjugate

#5/(8+sqrt7)*(8-sqrt7)/(8-sqrt7)#

combine

#(5*(8 - sqrt7))/((8*8)-sqrt7*sqrt7)#

Collect terms

#(40-5sqrt7)/(64-7)# #rArr# #(40-5sqrt7)/(57)#

#~~0.47#

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Answer 2

Eva Abramson

To simplify the expression 5/(8+sqrt(7)), we can multiply both the numerator and denominator by the conjugate of the denominator, which is 8-sqrt(7). This will help eliminate the square root in the denominator.

By multiplying the numerator and denominator by 8-sqrt(7), we get:

5 * (8-sqrt(7)) / ((8+sqrt(7)) * (8-sqrt(7)))

Simplifying further:

= (40 - 5sqrt(7)) / (64 - 7)

= (40 - 5sqrt(7)) / 57

Therefore, the simplified form of 5/(8+sqrt(7)) is (40 - 5sqrt(7)) / 57.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.