What is 5/(3sqrt(2)+4) ?

The solution to 5/(3sqrt(2)+4) is (15sqrt(2)-20)/2

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simplify 5/(3sqrt(2)+4)

simplify

\frac{5}{3 2 + 4}

\frac{15 2 - 20}{2}

Decimal Notation

0.60660 \dots

Solution steps

\frac{5}{3 2 + 4}

Multiply by the conjugate

\frac{3 2 - 4}{3 2 - 4}

= \frac{5 ( 3 2 - 4 )}{( 3 2 + 4 ) ( 3 2 - 4 )}

Expand

5 (32 - 4) : 152 - 20

Expand

(32 + 4) (32 - 4) : 2

= \frac{15 2 - 20}{2}

(3 x y + 4 z)^{2}

(1 + 7 i) - (12 - 8 i)

(x^{5} y^{4})^{\frac{1}{2}}

- 9 (4 p - 6 q) + 8 q - 7 (3 q - 3 p)

\frac{2 + 5 + 15}{2 + 5 + 3}