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6root(3)(5)+2root(3)(40)

$6 \sqrt[3]{5}+2 \sqrt[3]{40}$

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Multiply powers: integer bases

Full solution

Q.

6 \sqrt[3]{5}+2 \sqrt[3]{40}

Identify Terms: Identify the terms that can be combined. Both terms have a cube root, so they can be combined by adding the coefficients (the numbers in front of the cube roots).
Factor Out Cube Root: Factor out the cube root from the second term to simplify the expression. $2\sqrt{3}(40)$ can be written as $2\sqrt{3}(8\times 5)$ because $40$ is $8$ times $5$ .
Simplify Cube Root of $8$ : Simplify the cube root of $8$ . Since $8$ is a perfect cube $2 \times 2 \times 2$ , $\sqrt[3]{8}$ simplifies to $2$ . So $2\sqrt[3]{8 \times 5}$ becomes $2 \times 2\sqrt[3]{5}$ .
Multiply Coefficients: Multiply the coefficients in the second term. $2 \times 2\sqrt{3}(5)$ simplifies to $4\sqrt{3}(5)$ .
Combine Like Terms: Combine the like terms. $6\sqrt{3}(5) + 4\sqrt{3}(5)$ can be combined by adding the coefficients $6$ and $4$ , which gives us $10\sqrt{3}(5)$ .
Check for Further Simplification: Check if the cube root can be simplified further. Since $5$ is not a perfect cube, the cube root of $5$ cannot be simplified. Therefore, the expression remains $10\sqrt{3}(5)$ .

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