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Which of the following equals ?
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25 Aug 2018, 14:47
25 Aug 2018, 14:47
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Question Stats:
68% (00:32) correct
31% (00:45) wrong based on 85 sessions
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Which of the following equals \((\sqrt[2]{x})(\sqrt[3]{x})\)?
(A) \(\sqrt[5]{x}\)
(B) \(\sqrt[6]{x}\)
(C) \(\sqrt[3]{x^2}\)
(D) \(\sqrt[5]{x^6}\)
(E) \(\sqrt[6]{x^5}\)
(A) \(\sqrt[5]{x}\)
(B) \(\sqrt[6]{x}\)
(C) \(\sqrt[3]{x^2}\)
(D) \(\sqrt[5]{x^6}\)
(E) \(\sqrt[6]{x^5}\)
Re: Which of the following equals ?
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20 Mar 2020, 02:16
20 Mar 2020, 02:16
Why is it not (x^1/3)(x^1/2) to get 6th root X?
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Joined: 10 Apr 2015
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Re: Which of the following equals ?
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18 Jun 2020, 10:01
18 Jun 2020, 10:01
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sandy wrote:
Which of the following equals \((\sqrt[2]{x})(\sqrt[3]{x})\)?
(A) \(\sqrt[5]{x}\)
(B) \(\sqrt[6]{x}\)
(C) \(\sqrt[3]{x^2}\)
(D) \(\sqrt[5]{x^6}\)
(E) \(\sqrt[6]{x^5}\)
(A) \(\sqrt[5]{x}\)
(B) \(\sqrt[6]{x}\)
(C) \(\sqrt[3]{x^2}\)
(D) \(\sqrt[5]{x^6}\)
(E) \(\sqrt[6]{x^5}\)
Property #1: \(\sqrt[n]{x} = x^{\frac{1}{n}}\)
Property #2: \(x^{\frac{k}{n}} = (\sqrt[n]{x})^k= \sqrt[n]{x^k}\)
Given: \((\sqrt[2]{x})(\sqrt[3]{x})\)
Apply Property #1 to get: \((x^{\frac{1}{2}})(x^{\frac{1}{3}})\)
Since we're multiplying powers with the same base, we ADD the exponents to get: \(x^{(\frac{1}{2}+\frac{1}{3})}\)
Simplify to get: \(x^{\frac{5}{6}}\)
Apply Property #2 to get: \(\sqrt[6]{x^5}\)
Answer: E
Cheers,
Brent
