(27 + 243)/54 = ?

Question

\frac{√27+√243}{√54}=?

A. 2√2
B. 2√3
C. 3√2
D. 3√3
E. √2

BrentGMATPrepNow · Accepted Answer

We'll use the following rule: √(xy) = (√x)(√y)

√27 = √  = (√9)(√3) = 3√3
√243 = √  = (√81)(√3) = 9√3
√54 = √  = (√9)(√6) = 3√6

So, (√27 + √243)/√54 = (3√3 + 9√3)/(3√6)
= (12√3)/(3√6)
= 4/√2
Check answer choices.... not there.

Take 4/√2 and multiply top and bottom by  √2 .
We get: (4/√2)( √2 / √2 ) = (4√2)/(2) = 2√2 = A

Cheers,
Brent

Abhishek009 · Answer

\sqrt{27}  =  3\sqrt{3}

\sqrt{243}  =  9\sqrt{3}

\sqrt{54}  =  3\sqrt{3}\sqrt{2}

\sqrt{27}  +  \sqrt{243}  =  3\sqrt{3}  +  9\sqrt{3}

\sqrt{27}  +  \sqrt{243}  =  12\sqrt{3}

(  \sqrt{27}  +  \sqrt{243}  ) /  \sqrt{54}  = (  12\sqrt{3}  ) / (  3\sqrt{3}\sqrt{2}  )

3\sqrt{3}\sqrt{2}  =  4/\sqrt{2}  =  2\sqrt{2} 
 
Hence answer will be (A)

MathRevolution · Answer

(√27+√243)/√54=(3√3+9√3)/3√6=12√3/3√6=4/√2=2√2. Hence, the correct answer is A.

cicerone · Answer

Once you notice the following, figuring out the exact value of each of the given values can be eliminated and that should save some time

\frac{\sqrt{27} + \sqrt{243}}{\sqrt{54}} = \frac{ \sqrt{27} + ( \sqrt{27} imes \sqrt{9} ) } { \sqrt{27} imes \sqrt{2} } = \frac{ \sqrt{27} ( 1 + \sqrt{9} ) } { \sqrt{27} imes \sqrt{2} } = \frac{4}{\sqrt{2}} = 2\sqrt{2}

SQUINGEL · Answer

I still don't see how 12√3)/(3√6) gives 2√2

gracie90 · Answer

Could you or somebody please explain how 4 divided by square root of 2 equals 2 times square root of 2? Not sure why but I don't get it.

Bunuel · Answer

Multiply \frac{4}{\sqrt{2}} by \frac{\sqrt{2}}{\sqrt{2}} to get \frac{4}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2} This algebraic manipulation is called rationalization and is performed to eliminate irrational expression in the denominator. Questions involving rationalization to practice: if-x-0-then-106291.html if-n-is-positive-which-of-the-following-is-equal-to-31236.html consider-a-quarter-of-a-circle-of-radius-16-let-r-be-the-131083.html in-the-diagram-not-drawn-to-scale-sector-pq-is-a-quarter-139282.html in-the-diagram-what-is-the-value-of-x-129962.html the-perimeter-of-a-right-isoscles-triangle-is-127049.html which-of-the-following-is-equal-to-98531.html if-x-is-positive-then-1-root-x-1-root-x-163491.html 1-2-sqrt3-64378.html if-a-square-mirror-has-a-20-inch-diagonal-what-is-the-99359.html Hope it helps.

ScottTargetTestPrep · Answer

We are given (√27+√243)/√54. Let’s simplify each term.

√27 = √9 x √3 = 3√3

√243 = √81 x √3 = 9√3

√54 = √9 x √6 = 3√6

Thus:

(√27+√243)/√54 = (3√3 + 9√3)/(3√6) = (12√3)/(3√6) = 4/√2

Finally, we can rationalize 4/√2 by multiplying the numerator and denominator by √2 and we obtain:

(4/√2)(√2/√2) = (4√2)/2 = 2√2

Answer: A

mimajit · Answer

This is how i solved

√27+√243)/√54 =

First take out the factors for √27 , √243 and √ 54

Eg factors for √27 = √ 3*3*3 = 3√3 similarly for √ 243 = 9√3 and for √54 = 3√6

= ( 3√3 +9√3) / 3√6 = 12√3 / 3√6 = 4/√2 ,,,,, now check ans choice but we dont have the ans choice in this form so futher simplify'

= 2*2/√2 and we also know that √2* √2 =2 so lets write one of the 2 in √ form

= √2*√2 *2 / √2 cancel √2 from numerator and denoiminator to get 2√2 = ans choice A

avirupm97 · Answer

As simple as these questions seem to be, they always make my head

. Personally I don't like to see fractions as powers so there's a slightly alternate way that I follow which makes it seem way less complicated(at least for me

) Hope others like it : (√27+√243)/√54 => 27^1/2 + 243^1/2 / (3^3 * 2)^1/2 => 3^3/2 + 3^5/2 / 3^3/2 * √2 => Substituting √3 = A... => A^3 + A^5 / A^3 * √2 ....(Now brain is working again) => A^3 * (1 + A^2) / A^3 * √2 Taking A^3 as common => (1 + A^2) / √2 => 1+ (√3)^2 / √2 ....(Substituting back) => 4/√2 => 2√2

RohanNewDelhi · Answer

1. Simplify the radicals in the numerator
Find the largest perfect square factor for each number under the root:
 
  For √27:  The largest perfect square is 9. √27 = √(9 × 3) = √9 × √3 =  3√3  
  For √243:  The largest perfect square is 81. √243 = √(81 × 3) = √81 × √3 =  9√3   
Add them together to get the simplified numerator:  3√3 + 9√3 = 12√3 
2. Simplify the radical in the denominator
Find the largest perfect square factor for 54: The largest perfect square is 9.  √54 = √(9 × 6) = √9 × √6 = 3√6 
3. Divide the numerator by the denominator
Substitute the simplified forms back into the original fraction:  12√3 / 3√6 
First, divide the integers outside the roots:  12 / 3 = 4 
Now you have:  4√3 / √6 
To simplify the roots, you can rewrite √6 as √3 × √2:  4√3 / (√3 × √2) 
The √3 terms cancel out:  4 / √2 
4. Rationalize the denominator
To remove the square root from the denominator, multiply the top and bottom by √2:  (4 × √2) / (√2 × √2) = 4√2 / 2 
Divide by 2:  2√2 
The correct answer is  A .

(27 + 243)/54 = ?

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(27 + 243)/54 = ?

Prep Toolkit

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