What is 8/(8-sqrt(7)) ?

The solution to 8/(8-sqrt(7)) is (64+8sqrt(7))/(57)

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simplify 8/(8-sqrt(7))

simplify

\frac{8}{8 - 7}

\frac{64 + 8 7}{57}

Decimal Notation

1.49414 \dots

Solution steps

\frac{8}{8 - 7}

Multiply by the conjugate

\frac{8 + 7}{8 + 7}

= \frac{8 ( 8 + 7 )}{( 8 - 7 ) ( 8 + 7 )}

Expand

8 (8 + 7) : 64 + 87

Expand

(8 - 7) (8 + 7) : 57

= \frac{64 + 8 7}{57}

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