(27)^(1/3)/(9)^(1/2) =

Question

\small \frac{\sqrt {27}}{\sqrt{9}}=

A.   \small 1

B.  \small 2

C.   \small \sqrt{3}

D.  \small \sqrt {3}

E.  \small \frac{1}{\sqrt {3}}

Source: GMAP Prep

MarmikUpadhyay · Answer

\sqrt {27}/\sqrt{9} =?

27 = 3 * 3 * 3 =  3^3 
9 = 3 * 3 =  3^2

\sqrt {27}  =  \sqrt {3^3}  =  (3^3)^\frac{1}{3}  = 3
 \sqrt{9}  =  \sqrt{3^2}  =  (3^2)^\frac{1}{2}  = 3

=> \sqrt {27}/\sqrt{9}  =  \frac{3}{3}  = 1

So, correct answer is option  A .

MathRevolution · Answer

The cube root of 27 is 3 and the square root of 9 is 3.

=>  \frac{3}{3} = 1

Answer A

rachelphwu · Answer

Though the only acceptable option here is 1, 
since the square root of 9 can be 3 or -3, can I say "1 or -1" is the ultimate correct answer?

rachelphwu · Answer

Oh... I just found that the square root from a positive number is always positive.
That explains what 1 is the only answer.

Abhishek009 · Answer

\small \frac{\sqrt {27}}{\sqrt{9}}=  , Answer will be (A) 1

Or,  \small \frac{\sqrt {3^3}}{3}

Or,  \frac{3}{3} = 1

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