Simplify \[ \sqrt{\frac{2}{3} \times a^5} \] Circle your answer. - AQA - A-Level Maths Mechanics - Question 2 - 2019 - Paper 2

To simplify the expression, we first handle the components under the square root:

1. Separate the constant and variable terms: [ \sqrt{\frac{2}{3}} \times \sqrt{a^5} ]

2. Next, simplify (\sqrt{a^5}): [ a^5 = a^{4 + 1} = a^4 \times a = (a^2)^2 \times a ]

   • Thus, (\sqrt{a^5} = a^2 \sqrt{a}).

3. Now, we can combine everything together: [ \sqrt{\frac{2}{3}} \times a^2 \sqrt{a} ]

4. The final expression can then be rewritten using the notation for exponentiation:

   • The simplified form of (\sqrt{a}) is equal to (a^{\frac{1}{2}}), so: [ \sqrt{\frac{2}{3}} \times a^2 imes a^{\frac{1}{2}} = \sqrt{\frac{2}{3}} \times a^{2 + \frac{1}{2}} = \sqrt{\frac{2}{3}} \times a^{\frac{5}{2}} ]

Therefore, the answer will depend on the specific format required, but typically it would be presented as (a^{\frac{5}{2}}) or the above expression depending on further simplification.