Question

What is the following product? RootIndex 3 StartRoot 24 EndRoot times RootIndex 3 StartRoot 45 EndRoot.

Answer 1

The roots of same index and the values inside roots are real numbers, thus they can be combined under single root.

The product of given expression will be $6\:^3\sqrt{5}$

Given that:

• To find the product $^3\sqrt{24}\: \times\: ^3\sqrt{45}$

Evaluation:

Since both 24 and 45 are real numbers and since the root is of 3 index, thus we can combine both operands under multiplication under cube root.

Thus, we will have:

$\begin{aligned}^3\sqrt{24}\: \times\: ^3\sqrt{45} &=\: ^3\sqrt{24 \times 45} \\&= \: ^3\sqrt{4 \times 6 \times 15 \times 3}\\&= \: ^3\sqrt{2^3 \times 3^3 \times 5}\\&= 2 \times 3 \times \: ^3\sqrt{5}\\&= 6\:^3\sqrt{5}\end{aligned}$

Thus, the product result would be $6\:^3\sqrt{5}$

Learn more about cube root related products here:

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