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$\sqrt{14} + \sqrt{24}$

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Cube roots of positive perfect cubes

Full solution

Q.

\sqrt{14} + \sqrt{24}

Simplify $\sqrt{14}$ : Simplify $\sqrt{14}$ . $\sqrt{14} = \sqrt{2 \times 7}$ Can't simplify further.
Simplify $\sqrt{24}$ : Simplify $\sqrt{24}$ . $\sqrt{24} = \sqrt{4 \times 6}$ $\sqrt{24} = \sqrt{4} \times \sqrt{6}$ $\sqrt{24} = 2 \times \sqrt{6}$
Add $\sqrt{14}$ and $2 \times \sqrt{6}$ : Add $\sqrt{14}$ and $2 \times \sqrt{6}$ .
$\sqrt{14} + 2 \times \sqrt{6} = \sqrt{2 \times 7} + 2 \times \sqrt{6}$
Oops, can't add them directly since they are not like terms.

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