23. A shed has dimensions, in metres, of height \( =\sqrt{5} \), width \( =\sqrt{6} \) and length \( =\frac{9}{\sqrt{2}} \) Find the volume of the shed. Give your answer in the form a \( \sqrt{ } 15 \), where a is an integer.

To find the volume of the shed, we use the formula for volume which is given by: \[ \text{Volume} = \text{height} \times \text{width} \times \text{length} \] Substituting in the dimensions: \[ \text{Volume} = \sqrt{5} \times \sqrt{6} \times \frac{9}{\sqrt{2}} \] First, we can simplify \(\sqrt{5} \times \sqrt{6}\): \[ \sqrt{5} \times \sqrt{6} = \sqrt{30} \] Next, we multiply by \(\frac{9}{\sqrt{2}}\): \[ \text{Volume} = \sqrt{30} \times \frac{9}{\sqrt{2}} = 9 \times \frac{\sqrt{30}}{\sqrt{2}} = 9 \times \sqrt{\frac{30}{2}} = 9 \times \sqrt{15} \] Thus, the volume of the shed is: \[ \text{Volume} = 9\sqrt{15} \] So, \( a = 9 \).