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Simplify  $\sqrt[3]{192}+5\sqrt[3]{64}$3√192+53√64​ .The simplified expression is .

Question

Simplify 1923+5643 \sqrt[3]{192} + 5\sqrt[3]{64}

The simplified expression is.

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Solution

To simplify the expression 1923+5643\sqrt[3]{192}+5\sqrt[3]{64}, we first need to simplify the cube roots.

The cube root of 192 can be simplified by finding the prime factorization of 192, which is 26∗32^6 * 3. We can then group these factors into triples, which gives us 22∗332^2 * \sqrt[3]{3}, or 4 cube root of 3.

The cube root of 64 is 4, because 43=644^3 = 64.

So, the simplified expression is 433+5∗44\sqrt[3]{3} + 5*4, or 433+204\sqrt[3]{3} + 20.

This problem has been solved

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