What is 4/(sqrt(7-\sqrt{5))} ?

The solution to 4/(sqrt(7-\sqrt{5))} is ((7+sqrt(5))sqrt(7-\sqrt{5)})/(11)

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simplify 4/(sqrt(7-\sqrt{5))}

simplify

\frac{4}{7 - 5}

\frac{( 7 + 5 ) 7 - 5}{11}

Decimal Notation

1.83264 \dots

Solution steps

\frac{4}{7 - 5}

Multiply by the conjugate

\frac{7 - 5}{7 - 5}

= \frac{4 7 - 5}{7 - 5 7 - 5}

7 - 5 7 - 5 = 7 - 5

= \frac{4 7 - 5}{7 - 5}

Multiply by the conjugate

\frac{7 + 5}{7 + 5}

= \frac{4 7 - 5 ( 7 + 5 )}{( 7 - 5 ) ( 7 + 5 )}

(7 - 5) (7 + 5) = 44

= \frac{4 ( 7 + 5 ) 7 - 5}{44}

Cancel the common factor:

4

= \frac{( 7 + 5 ) 7 - 5}{11}

- 5 0^{2}

58 \times 34

\frac{5}{8} \times \frac{1}{2}

lo g_{16} (\frac{1}{32})

1 - \frac{7}{9}

What is 4/(sqrt(7-\sqrt{5))} ?
The solution to 4/(sqrt(7-\sqrt{5))} is ((7+sqrt(5))sqrt(7-\sqrt{5)})/(11)