How do you rationalise the denominator of 6/(3√2)?

To rationalise the denominator of \( \frac{6}{3\sqrt{2}} \), multiply the numerator and the denominator by \( \sqrt{2} \).

Rationalising the denominator means getting rid of the square root in the denominator. In this case, you have \( \frac{6}{3\sqrt{2}} \). To do this, you multiply both the numerator and the denominator by \( \sqrt{2} \). This is because \( \sqrt{2} \times \sqrt{2} = 2 \), which is a rational number.

So, let's multiply the numerator and the denominator by \( \sqrt{2} \):

\[ \frac{6}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{6\sqrt{2}}{3\sqrt{2} \times \sqrt{2}} \]

Now, simplify the denominator:

\[ 3\sqrt{2} \times \sqrt{2} = 3 \times 2 = 6 \]

So, the expression becomes:

\[ \frac{6\sqrt{2}}{6} \]

Next, simplify the fraction by dividing both the numerator and the denominator by 6:

\[ \frac{6\sqrt{2}}{6} = \sqrt{2} \]

Therefore, the rationalised form of \( \frac{6}{3\sqrt{2}} \) is \( \sqrt{2} \).