Perform the indicated operations. Assume all variables represent positive real numbers. 233+4243−8132\sqrt[3]{3} + 4\sqrt[3]{24} - \sqrt[3]{81} 233+4324−381

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 99

1장, 문제 99

Perform the indicated operations. Assume all variables represent positive real numbers. $2$\sqrt$[3]{3} + 4$\sqrt$[3]{24} - $\sqrt$[3]{81}$

검증된 단계별 안내

Identify the cube roots in the expression: $2\sqrt[3]{3} + 4\sqrt[3]{24} - \sqrt[3]{81}$.

Simplify each cube root by factoring the radicand into prime factors and extracting perfect cubes: For example, $\sqrt[3]{24} = \sqrt[3]{8 \times 3}$ and $\sqrt[3]{81} = \sqrt[3]{27 \times 3}$.

Rewrite the expression using the simplified cube roots: $2\sqrt[3]{3} + 4\sqrt[3]{8 \times 3} - \sqrt[3]{27 \times 3}$.

Extract the cube roots of the perfect cubes: $\sqrt[3]{8} = 2$ and $\sqrt[3]{27} = 3$, then rewrite the terms accordingly.

Combine like terms by factoring out the common cube root $\sqrt[3]{3}$ and then perform the arithmetic operations on the coefficients.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Simplifying Radicals

Simplifying radicals involves expressing the radicand (the number inside the root) as a product of perfect powers and other factors. This allows you to extract perfect cubes (for cube roots) outside the radical, making the expression easier to work with and combine.

Like Radicals and Combining Terms

Only radicals with the same index and radicand can be combined through addition or subtraction. After simplifying, identify like radicals to add or subtract their coefficients, similar to combining like terms in algebra.

Properties of Cube Roots

The cube root of a product equals the product of the cube roots: ∛(a·b) = ∛a · ∛b. This property helps break down complex radicands into simpler parts, facilitating simplification and combination of terms.

Perform the indicated operations. Assume all variables represent positive real numbers. 233+4243−8132\(\sqrt\)[3]{3} + 4\(\sqrt\)[3]{24} - \(\sqrt\)[3]{81} 233+4324−381

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Simplifying Radicals

Like Radicals and Combining Terms

Properties of Cube Roots

Perform the indicated operations. Assume all variables represent positive real numbers. $2\(\sqrt\)[3]{3} + 4\(\sqrt\)[3]{24} - \(\sqrt\)[3]{81}$