What is (sqrt(5+2\sqrt{6)})/(sqrt(5-2\sqrt{6))} ?

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

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simplify (sqrt(5+2\sqrt{6)})/(sqrt(5-2\sqrt{6))}

simplify

\frac{5 + 2 6}{5 - 2 6}

26 + 5

Decimal Notation

9.89897 \dots

Solution steps

\frac{5 + 2 6}{5 - 2 6}

Apply radical rule:

\frac{a}{b} = \frac{a}{b}, a \geq 0, b \geq 0

\frac{5 + 2 6}{5 - 2 6} = \frac{5 + 2 6}{5 - 2 6}

= \frac{5 + 2 6}{5 - 2 6}

Cancel

\frac{5 + 2 6}{5 - 2 6} : 49 + 206

= 49 + 206

= 24 + 206 + 25

= 4 \cdot 6 + 206 + 25

= (4)^{2} (6)^{2} + 206 + (25)^{2}

4 = 2

25 = 5

= 2^{2} (6)^{2} + 206 + 5^{2}

2 \cdot 26 \cdot 5 = 206

= (26)^{2} + 2 \cdot 26 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(26)^{2} + 2 \cdot 26 \cdot 5 + 5^{2} = (26 + 5)^{2}

= (26 + 5)^{2}

Apply radical rule:

(26 + 5)^{2} = 26 + 5

= 26 + 5

(x^{2} - 1) \cdot (x^{2} - 1)

\frac{e ^{x}}{e ^{4 x}}

(3 + 1) (1 + 3)

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