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

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

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

rationalize

\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 7 ( 3 - 7 )}{( 3 + 7 ) ( 3 - 7 )}

27 (3 - 7) = 67 - 14

(3 + 7) (3 - 7) = 2

= \frac{6 7 - 14}{2}

Factor

67 - 14 : 2 (37 - 7)

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

Divide the numbers:

\frac{2}{2} = 1

= 37 - 7

3 x^{2} - 2 x^{3}

3^{5} \times 3^{2}

\frac{20}{18}

- 3 x^{2} + 18 x - 24

- \frac{20}{8}

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