How do you rationalise the denominator of 5/√2?

To rationalise the denominator of \( \frac{5}{\sqrt{2}} \), multiply both the numerator and the denominator by \( \sqrt{2} \).

When you have a fraction like \( \frac{5}{\sqrt{2}} \), the denominator contains a surd (a square root that cannot be simplified to a whole number). To rationalise the denominator, you need to eliminate the surd. This is done by multiplying both the numerator and the denominator by the same surd, in this case, \( \sqrt{2} \).

Here's the step-by-step process:

1. Start with the original fraction: \( \frac{5}{\sqrt{2}} \).
2. Multiply both the numerator and the denominator by \( \sqrt{2} \):
\[ \frac{5 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} \].
3. Simplify the denominator: \( \sqrt{2} \times \sqrt{2} = 2 \).
4. This gives you: \( \frac{5\sqrt{2}}{2} \).

So, \( \frac{5}{\sqrt{2}} \) rationalises to \( \frac{5\sqrt{2}}{2} \). By doing this, you have removed the surd from the denominator, making the fraction easier to work with in further calculations.