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

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

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

simplify

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

3 + 2

Solution steps

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

Cancel

\frac{2 + 3}{2 - 3} : 7 + 43

= 7 + 43

= 3 + 43 + 4

= (3)^{2} + 43 + (4)^{2}

4 = 2

= (3)^{2} + 43 + 2^{2}

23 \cdot 2 = 43

= (3)^{2} + 23 \cdot 2 + 2^{2}

Apply Perfect Square Formula:

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

(3)^{2} + 23 \cdot 2 + 2^{2} = (3 + 2)^{2}

= (3 + 2)^{2}

Apply radical rule:

(3 + 2)^{2} = 3 + 2

= 3 + 2

lo g_{10} (7) - lo g_{10} (3) + lo g_{10} (6)

\frac{8}{x ^{2} + 6 x} \cdot 2 x

- \frac{2}{3} \cdot (- 1)

- 2 x (x^{2} - 3)

- 32 + 36 - 8

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