simplify 1/(sqrt(2)+sqrt(3)) — step-by-step solution

Let's reduce:

\frac{1}{\sqrt{2} + \sqrt{3}}

Multiply numerator and denominator by the conjugate

\sqrt{2} - \sqrt{3}

: (a+b)(a-b) = a²-b², here

{(\sqrt{2})}^{2} - {(\sqrt{3})}^{2}

2 - 3

-1

ⅰ

\frac{1}{\sqrt{2} + \sqrt{3}}

- (\sqrt{2} - \sqrt{3})

- (\sqrt{2} - \sqrt{3})

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (\sqrt{2} - \sqrt{3})

- \sqrt{2} + \sqrt{3}

- \sqrt{2} + \sqrt{3}

▶Simplified form:

\sqrt{3} - \sqrt{2}

The numeric value of:

\sqrt{3} - \sqrt{2}

equals:

\approx 1.7321 - \approx 1.4142

▷

\approx 0.3178