What is 4/(sqrt(2)+\sqrt{7)} ?

The solution to 4/(sqrt(2)+\sqrt{7)} is -(4sqrt(2)-4sqrt(7))/5

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simplify 4/(sqrt(2)+\sqrt{7)}

simplify

\frac{4}{2 + 7}

- \frac{4 2 - 4 7}{5}

Decimal Notation

0.98523 \dots

Solution steps

\frac{4}{2 + 7}

Multiply by the conjugate

\frac{2 - 7}{2 - 7}

= \frac{4 ( 2 - 7 )}{( 2 + 7 ) ( 2 - 7 )}

Expand

4 (2 - 7) : 42 - 47

Expand

(2 + 7) (2 - 7) : - 5

= \frac{4 2 - 4 7}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4 2 - 4 7}{5}

\frac{( - 1 ) ^{2 - 1}}{2 ^{2}}

3^{2 l o g_{3} (7)}

\frac{6}{5} + \frac{12}{35}

4 π 3^{2}

6 x^{3} - 15 x^{2} - 24 x + 60

What is 4/(sqrt(2)+\sqrt{7)} ?
The solution to 4/(sqrt(2)+\sqrt{7)} is -(4sqrt(2)-4sqrt(7))/5