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What is √363+√147 + √27?

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What is √363+√147 + √27? [#permalink]

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New post 25 Feb 2017, 07:05
1
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

94% (00:57) correct 6% (01:46) wrong based on 107 sessions

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What is √363+√147 + √27?

A) 6√6
(B) 7√6
(C) 11√3
(D) 21√3
(E) 30√3
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What is √363+√147 + √27? [#permalink]

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New post Updated on: 25 Feb 2017, 07:17
vikasp99 wrote:
What is √363+√147 + √27?

A) 6√6
(B) 7√6
(C) 11√3
(D) 21√3
(E) 30√3


√363+√147 + √27
= √121*√3+√49*√3+√9*√3
= (11+7+3)*√3
= 21√3

Hence option D is correct
Hit Kudos if you liked it 8-)

Originally posted by 0akshay0 on 25 Feb 2017, 07:10.
Last edited by 0akshay0 on 25 Feb 2017, 07:17, edited 1 time in total.
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Re: What is √363+√147 + √27? [#permalink]

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New post 25 Feb 2017, 07:12
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Top Contributor
vikasp99 wrote:
What is √363 + √147 + √27?

A) 6√6
(B) 7√6
(C) 11√3
(D) 21√3
(E) 30√3


To simplify roots, we'll use the following rule: √(ab) = (√a)(√b)

√363 = √(121 x 3)
= (√121)(√3)
= 11√3

√147 = √(49 x 3)
= (√49)(√3)
= 7√3

√27 = √(9 x 3)
= (√9)(√3)
= 3√3

So, √363 + √147 + √27 = 11√3 + 7√3 + 3√3
= 21√3

Answer: D

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Re: What is √363+√147 + √27? [#permalink]

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New post 25 Feb 2017, 12:40
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vikasp99 wrote:
What is √363+√147 + √27?

A) 6√6
(B) 7√6
(C) 11√3
(D) 21√3
(E) 30√3


No reason not to estimate! The answer choices are very far apart. If you're better with reasoning than with arithmetic, give this a try:

√363 is a bit less than √400, so let's say it's about 20
√147 is a bit more than √144, so it's about 12
√27 is a bit more than √25, so it's about 5

20 + 12 + 5 = 37. We want 37 as an answer...

6√6 and 7√6 are definitely too small. The square root of 6 is only around 2.5-ish. To make 6 or 7 into 37, we'd have to multiply them by something much larger than √6.

11√3 is also too small. √3 is less than 2, so this answer will be less than 22.

30√3 is too large, since it'll be in the neighborhood of 1.5*30 = 45.

(D) is correct.
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Re: What is √363+√147 + √27? [#permalink]

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New post 26 Feb 2017, 00:08
vikasp99 wrote:
What is √363+√147 + √27?

A) 6√6
(B) 7√6
(C) 11√3
(D) 21√3
(E) 30√3


\(√3*11^2+√7^2*3 + √3^3\)

\(= 11√3 + 7√3 + 3√3\)

\(= 21√3\)

Thus, answer must be (D) \(21√3\)
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Re: What is √363+√147 + √27?   [#permalink] 26 Feb 2017, 00:08
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What is √363+√147 + √27?

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