What is (4+2sqrt(7))/(3-sqrt(7)) ?

The solution to (4+2sqrt(7))/(3-sqrt(7)) is 13+5sqrt(7)

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simplify (4+2sqrt(7))/(3-sqrt(7))

simplify

\frac{4 + 2 7}{3 - 7}

13 + 57

Decimal Notation

26.22875 \dots

Solution steps

\frac{4 + 2 7}{3 - 7}

Multiply by the conjugate

\frac{3 + 7}{3 + 7}

= \frac{( 4 + 2 7 ) ( 3 + 7 )}{( 3 - 7 ) ( 3 + 7 )}

Expand

(4 + 27) (3 + 7) : 26 + 107

Expand

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

= \frac{26 + 10 7}{2}

Factor out common term

2 : 2 (13 + 57)

= \frac{2 ( 13 + 5 7 )}{2}

Cancel the common factor:

2

= 13 + 57

lo g_{10} (4) (8)

0.0394 \div 100

\frac{76}{6}

\frac{5}{45}

What is (4+2sqrt(7))/(3-sqrt(7)) ?
The solution to (4+2sqrt(7))/(3-sqrt(7)) is 13+5sqrt(7)