What is 363^(1/2) + 147^(1/2) + 27^(1/2)

Question

What is  \sqrt{363} + \sqrt{147}+ \sqrt{27}

A.  6\sqrt{6}

B.  7\sqrt{6}

C.  11\sqrt{3}

D.  21\sqrt{3}

E.  30\sqrt{3}

0akshay0 · Answer

√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-)

BrentGMATPrepNow · Answer

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

ccooley · Answer

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.

Abhishek009 · Answer

√3*11^2+√7^2*3 + √3^3

= 11√3 + 7√3 + 3√3

= 21√3

Thus, answer must be (D)  21√3

14101992 · Answer

root(363) = 11 * root (3)
root (147) = 7 * root (3)
root (27) = 3 * root (3)

adding them, we get 21 root(3)

Hence, D will be the answer.

singhabhijeet · Answer

\sqrt{{363}} +\sqrt{{147}} + \sqrt{{27}}

363 = 11*11*3
147 = 7*7*3
27 = 3*3*3

=  11\sqrt{{3}} + 7\sqrt{{3}} + 3\sqrt{{3}}

=  21\sqrt{{3}}

Ans : Option D

JS1290 · Answer

363- Square root of 3 * Square root of 121 - 11 root 3
147- Square root of 49 * Square root of 3 - 7 root 3
27- Square root of 9 * Square root of 3 - 3 root 3

Add of these up (11 root 3 + 7 root 3 + 3 root 3) and we will get 21 root 3; Hence D

stonecold · Answer

Nice one Bunuel.
Here is what i did on this one ->

\sqrt{363} + \sqrt{147}+ \sqrt{27}

=> 11√3 + 7√3 + 3√3

=> √3(11+7+3)

=> √3*21

=> 21√3

SMASH THAT D.

JeffTargetTestPrep · Answer

Let’s simplify each root:

√363 = √121 x √3 = 11√3

√147 = √49 x √3 = 7√3

√27 = √9 x √3 = 3√3

Thus, we have:

11√3 + 7√3 + 3√3 = 21√3

Answer: D

AkshdeepS · Answer

\sqrt{363} + \sqrt{147}+ \sqrt{27}

\sqrt{11*11*3 + 7*7*3 + 3*3*3}

11*\sqrt{3} + 7*\sqrt{3} + 3*\sqrt{3}

21*\sqrt{3}

(D)

Snehaaaaa · Answer

Explanation-
363 = 11*11*3
147 = 7*7*3
27 = 3*3*3
Therefore expression = 11 \sqrt{3}  + 7 \sqrt{3}  + 3 \sqrt{3} 
=  \sqrt{3} (11+7+3)
=21 \sqrt{3}

What is 363^(1/2) + 147^(1/2) + 27^(1/2)

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is 363^(1/2) + 147^(1/2) + 27^(1/2)

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards