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

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

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

simplify

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

2 + 6

Decimal Notation

4.44948 \dots

Solution steps

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

Multiply by the conjugate

\frac{3 3 + 2 2}{3 3 + 2 2}

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

Expand

(23 + 52) (33 + 22) : 38 + 196

Expand

(33 - 22) (33 + 22) : 19

= \frac{38 + 19 6}{19}

Factor out common term

19 : 19 (2 + 6)

= \frac{19 ( 2 + 6 )}{19}

Cancel the common factor:

19

= 2 + 6

5 n^{2} + 4 n - 10305

0^{\frac{2}{3}}

600 = (x \cdot 0.06) + x

\frac{2 1 ^{6} \cdot 3 5 ^{3} \cdot 8 0 ^{3}}{1 5 ^{4} \cdot 1 4 ^{9} \cdot 3 0 ^{2}}

2 x + 4 = 11

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