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

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

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simplify (2sqrt(7))/(3+sqrt(7))

simplify

\frac{2 7}{3 + 7}

37 - 7

Decimal Notation

0.93725 \dots

Solution steps

\frac{2 7}{3 + 7}

Multiply by the conjugate

\frac{3 - 7}{3 - 7}

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

Expand

2 (3 - 7) : 6 - 27

Expand

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

= \frac{( 6 - 2 7 ) 7}{2}

Factor out common term

2 : 2 (3 - 7)

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

Cancel the common factor:

2

= (3 - 7) 7

(3 - 7) 7 = 37 - 7

= 37 - 7

+ (x^{2} + x - 20)

\frac{1}{4} \times 100

\frac{- i}{1 - i}

\frac{( 1520000 - 95000 )}{10}

\frac{4}{38}

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