simplify sqrt(5)/(sqrt(6)-2) — step-by-step solution

Let's reduce:

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

Multiply numerator and denominator by the conjugate

\sqrt{6} + 2

: (a+b)(a-b) = a²-b², here

{(\sqrt{6})}^{2} - 2^{2}

6 - 4

2

ⅰ

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

\frac{\sqrt{5} \times (\sqrt{6} + 2)}{2}

\frac{\sqrt{5} \times (\sqrt{6} + 2)}{2}

▶Simplified form:

\frac{\sqrt{5} \times (2 + \sqrt{6})}{2}

The numeric value of:

\frac{\sqrt{5} \times (2 + \sqrt{6})}{2}

is:

\frac{\approx 2.2361 \times (2 + \approx 2.4495)}{2}

\frac{\approx 2.2361 \times \approx 4.4495}{2}

\frac{\approx 9.9494}{2}

▷

\approx 4.9747