What is (2sqrt(3)+7sqrt(2))/(5sqrt(3)-4\sqrt{2)} ?

The solution to (2sqrt(3)+7sqrt(2))/(5sqrt(3)-4\sqrt{2)} is 2+sqrt(6)

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simplify (2sqrt(3)+7sqrt(2))/(5sqrt(3)-4\sqrt{2)}

simplify

\frac{2 3 + 7 2}{5 3 - 4 2}

2 + 6

Decimal Notation

4.44948 \dots

Solution steps

\frac{2 3 + 7 2}{5 3 - 4 2}

Multiply by the conjugate

\frac{5 3 + 4 2}{5 3 + 4 2}

= \frac{( 2 3 + 7 2 ) ( 5 3 + 4 2 )}{( 5 3 - 4 2 ) ( 5 3 + 4 2 )}

Expand

(23 + 72) (53 + 42) : 86 + 436

Expand

(53 - 42) (53 + 42) : 43

= \frac{86 + 43 6}{43}

Factor out common term

43 : 43 (2 + 6)

= \frac{43 ( 2 + 6 )}{43}

Cancel the common factor:

43

= 2 + 6

2 - 2 cos (θ)

lo g_{25} (8)

7 \cdot \frac{1}{3}

(e^{i x})^{2}

\frac{a - 4 + \frac{4}{a}}{1 - \frac{2}{a}}

What is (2sqrt(3)+7sqrt(2))/(5sqrt(3)-4\sqrt{2)} ?
The solution to (2sqrt(3)+7sqrt(2))/(5sqrt(3)-4\sqrt{2)} is 2+sqrt(6)