What is 7/(3+sqrt(2)) ?

The solution to 7/(3+sqrt(2)) is 3-sqrt(2)

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simplify 7/(3+sqrt(2))

simplify

\frac{7}{3 + 2}

3 - 2

Decimal Notation

1.58578 \dots

Solution steps

\frac{7}{3 + 2}

Multiply by the conjugate

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

= \frac{7 ( 3 - 2 )}{( 3 + 2 ) ( 3 - 2 )}

Expand

7 (3 - 2) : 21 - 72

Expand

(3 + 2) (3 - 2) : 7

= \frac{21 - 7 2}{7}

Factor out common term

7 : 7 (3 - 2)

= \frac{7 ( 3 - 2 )}{7}

Cancel the common factor:

7

= 3 - 2

\frac{7}{12} + \frac{5}{9}

2 (x + 1)^{2} + 1

6 n^{2} - 9 n

- (- 10 k + 8.8 m + 10)

\frac{2}{7} \div \frac{1}{2}