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

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.

\(√3*11^2+√7^2*3 + √3^3\)

\(= 11√3 + 7√3 + 3√3\)

\(= 21√3\)

Thus, answer must be (D) \(21√3\)

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.

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

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

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

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.

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

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

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

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

\(21*\sqrt{3}\)

(D)

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\(\sqrt{3}\)