How do you simplify $4 \sqrt[3]{135}$ $4root3(135)$ ?

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Answer 1 · 2017-05-01T17:12:30

See the solution process below:

We can use this rule for radicals to rewrite the expression:

$\sqrt[n]{a \cdot b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$ $root(n)(a * b) = root(n)(a) * root(n)(b)$

$4 \sqrt[3]{135} = 4 \sqrt[3]{27 \cdot 5} = 4 \sqrt[3]{27} \sqrt[3]{5}$ $4root(3)(135) = 4root(3)(27 * 5) = 4root(3)(27)root(3)(5)$

We can now simplify $\sqrt[3]{27} = 3$ $root(3)(27) = 3$ to write:

$4 \sqrt[3]{27} \sqrt[3]{5} = (4 \cdot 3) \sqrt[3]{5} = 12 \sqrt[3]{5}$ $4root(3)(27)root(3)(5) = (4 * 3)root(3)(5) = 12root(3)(5)$

How do you simplify 43√1354root3(135)?