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Step-by-step Solution

Rationalize the denominator $\frac{5}{\sqrt{2}}$

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Answer

$\frac{5\sqrt{2}}{2}$$\,\,\left(\approx 3.5355339059327378\right)$

Step-by-step explanation

Problem to solve:

$\frac{5}{\sqrt{2}}$
1

To rationalize the denominator of the fraction, we multiply the numerator and denominator by $\sqrt{2}$

$\frac{5}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}$
2

Multiplying fractions

$\frac{5\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}$
3

When multiplying two powers that have the same base ($\sqrt{2}$), you can add the exponents

$\frac{5\cdot \sqrt{2}}{\left(\sqrt{2}\right)^2}$
4

Cancel exponents $\frac{1}{2}$ and $2$

$\frac{5\sqrt{2}}{2}$

Answer

$\frac{5\sqrt{2}}{2}$$\,\,\left(\approx 3.5355339059327378\right)$

Problem Analysis

$\frac{5}{\sqrt{2}}$

Main topic:

Rationalisation

Time to solve it:

~ 0.3 seconds

Related topics:

Rationalisation