근호를 포함한 식의 계산 연습문제 — OpenStax Intermediate Algebra · 8.4절 · 3번

OpenStax Intermediate Algebra · 8.4절 · 3번우리말 번역

간단히 하세요: ⓐ $\sqrt{20}+3\sqrt{5}$ ⓑ $\sqrt[3]{24}-\sqrt[3]{375}$ ⓒ $\frac{1}{2}\sqrt[4]{48}-\frac{2}{3}\sqrt[4]{243}.$

영어 원문 보기

Simplify: ⓐ $\sqrt{20}+3\sqrt{5}$ ⓑ $\sqrt[3]{24}-\sqrt[3]{375}$ ⓒ $\frac{1}{2}\sqrt[4]{48}-\frac{2}{3}\sqrt[4]{243}.$

정답·풀이 보기

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	$\quad \sqrt[3]{24}-\sqrt[3]{375}$
근호를 간단히 한다.	$\quad \sqrt[3]{8}\cdot \sqrt[3]{3}-\sqrt[3]{125}\cdot \sqrt[3]{3}$
	$\quad 2\,\sqrt[3]{3}-5\,\sqrt[3]{3}$
동류의 근호끼리 계산한다.	$\quad -3\sqrt[3]{3}$

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	$\quad \frac{1}{2}\,\sqrt[4]{48}-\frac{2}{3}\,\sqrt[4]{243}$
근호를 간단히 한다.	$\quad \frac{1}{2}\,\sqrt[4]{16}\cdot \sqrt[4]{3}-\frac{2}{3}\,\sqrt[4]{81}\cdot \sqrt[4]{3}$
	$\quad \frac{1}{2}\cdot 2\cdot \sqrt[4]{3}-\frac{2}{3}\cdot 3\cdot \sqrt[4]{3}$
	$\quad \sqrt[4]{3}-2\,\sqrt[4]{3}$
동류의 근호끼리 계산한다.	$\quad -\sqrt[4]{3}$

원본 교재 풀이(영어)

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	$\quad \sqrt{20}+3\,\sqrt{5}$
Simplify the radicals, when possible.	$\quad \sqrt{4}\cdot \sqrt{5}+3\,\sqrt{5}$
	$\quad 2\,\sqrt{5}+3\,\sqrt{5}$
Combine the like radicals.	$\quad 5\,\sqrt{5}$

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	$\quad \sqrt[3]{24}-\sqrt[3]{375}$
Simplify the radicals.	$\quad \sqrt[3]{8}\cdot \sqrt[3]{3}-\sqrt[3]{125}\cdot \sqrt[3]{3}$
	$\quad 2\,\sqrt[3]{3}-5\,\sqrt[3]{3}$
Combine the like radicals.	$\quad -3\sqrt[3]{3}$

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	$\quad \frac{1}{2}\,\sqrt[4]{48}-\frac{2}{3}\,\sqrt[4]{243}$
Simplify the radicals.	$\quad \frac{1}{2}\,\sqrt[4]{16}\cdot \sqrt[4]{3}-\frac{2}{3}\,\sqrt[4]{81}\cdot \sqrt[4]{3}$
	$\quad \frac{1}{2}\cdot 2\cdot \sqrt[4]{3}-\frac{2}{3}\cdot 3\cdot \sqrt[4]{3}$
	$\quad \sqrt[4]{3}-2\,\sqrt[4]{3}$
Combine the like radicals.	$\quad -\sqrt[4]{3}$

한 번 더 — 비슷한 문제OpenStax Intermediate Algebra · 8.5절 · 1번우리말 번역

간단히 하세요: ⓐ $\frac{\sqrt{50{s}^{3}}}{\sqrt{128s}}$ ⓑ $\frac{\sqrt[3]{56{a}^{}}}{\sqrt[3]{7{a}^{4}}}.$

답 쓰고 채점

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다 풀었으면 정답 확인

ⓐ $\frac{5s}{8}$ ⓑ $\frac{2}{a}$