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What is the difference between 150^(1/2) and 54^(1/2)

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Math Expert
Joined: 02 Sep 2009
Posts: 46176
What is the difference between 150^(1/2) and 54^(1/2) [#permalink]

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04 Mar 2018, 23:10
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Difficulty:

25% (medium)

Question Stats:

89% (00:42) correct 11% (01:15) wrong based on 34 sessions

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What is the difference between $$\sqrt{150}$$ and $$\sqrt{54}$$

(A) $$2\sqrt{6}$$

(B) $$16\sqrt{6}$$

(C) $$\sqrt{96}$$

(D) $$6\sqrt{2}$$

(E) $$8\sqrt{6}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 46176
Re: What is the difference between 150^(1/2) and 54^(1/2) [#permalink]

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04 Mar 2018, 23:50
Director
Joined: 21 May 2013
Posts: 646
Re: What is the difference between 150^(1/2) and 54^(1/2) [#permalink]

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05 Mar 2018, 04:12
Bunuel wrote:
What is the difference between $$\sqrt{150}$$ and $$\sqrt{54}$$

(A) $$2\sqrt{6}$$

(B) $$16\sqrt{6}$$

(C) $$\sqrt{96}$$

(D) $$6\sqrt{2}$$

(E) $$8\sqrt{6}$$

=5\sqrt{6}-3\sqrt{6}
=2\sqrt{6}
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Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3509
Location: India
GPA: 3.5
What is the difference between 150^(1/2) and 54^(1/2) [#permalink]

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05 Mar 2018, 07:01
Bunuel wrote:
What is the difference between $$\sqrt{150}$$ and $$\sqrt{54}$$

(A) $$2\sqrt{6}$$

(B) $$16\sqrt{6}$$

(C) $$\sqrt{96}$$

(D) $$6\sqrt{2}$$

(E) $$8\sqrt{6}$$

$$\sqrt{150} - \sqrt{54}$$

= $$\sqrt{5^2*3*2} - \sqrt{2*3^3}$$

= $$5\sqrt{6} - 3\sqrt{6}$$

= $$2\sqrt{6}$$, Answer must be (A)
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: What is the difference between 150^(1/2) and 54^(1/2) [#permalink]

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06 Mar 2018, 11:19
Bunuel wrote:
What is the difference between $$\sqrt{150}$$ and $$\sqrt{54}$$

(A) $$2\sqrt{6}$$

(B) $$16\sqrt{6}$$

(C) $$\sqrt{96}$$

(D) $$6\sqrt{2}$$

(E) $$8\sqrt{6}$$

We need to determine √150 - √54:

√150 - √54 = √25 x √6 - √9 x √6

5√6 - 3√6 = 2√6

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Re: What is the difference between 150^(1/2) and 54^(1/2)   [#permalink] 06 Mar 2018, 11:19
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