# Step-by-step Solution

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$\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

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

Rationalisation

~ 0.3 seconds