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High School
Algebra
Algebra I
Exponents and radicals

iohanetc

Answered question

2021-09-07

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.
$3 \sqrt[3]{4} (2 \sqrt[3]{2} - 6 \sqrt[3]{4})$

Answer & Explanation

escumantsu

Skilled2021-09-08Added 98 answers

Given expression:
$3 \sqrt[3]{4} (2 \sqrt[3]{2} - 6 \sqrt[3]{4})$
$3 \sqrt[3]{4} (2 \sqrt[3]{2} - 6 \sqrt[3]{4}) = 3 \sqrt[3]{4} (2 \sqrt[3]{2} - 3 \sqrt[3]{4}) (6 \sqrt[3]{4})$
$6 \sqrt[3]{4} \sqrt[3]{2} - 18 \sqrt[3]{4} \sqrt[3]{4}$
$= 6 \sqrt[3]{4 \times 2} - 18 \sqrt[3]{4 \times 4}$
$6 \sqrt[3]{8} - 18 \sqrt[3]{16}$
$= 6 {(8)}^{\frac{1}{3}} - 18 {(16)}^{\frac{1}{3}}$
$6 {(2 \times 2 \times 2)}^{\frac{1}{3}} - 18 {(2 \times 2 \times 2)}^{\frac{1}{3}}$
$= 6 (2) - 18 (2) {(2)}^{\frac{1}{3}}$
$= 12 - 36 {(2)}^{\frac{1}{3}}$
$= 12 - 36 {(2)}^{\frac{1}{3}}$
$= 12 - 36 \sqrt[3]{2}$
Hence
$3 \sqrt[3]{4} (2 \sqrt[3]{2} - 6 \sqrt[3]{4}) = 12 - 36 \sqrt[3]{2}$

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