If a 0, what is the value of a^(1/2)?

Question

If a > 0, what is the value of  a^{\frac{1}{2}} ?

(1)  a^{\frac{1}{8}}=16 
(2)  a^{\frac{1}{32}}=2

Hatakekakashi · Answer

looking at both the statements as a>0 
a unique value of a is possible and we can find the square root of that

(D) Imo

twoface07 · Answer

With a > 0, we can check the statements in the following manner:

Statement (1): Take  a^{\frac{1}{8}}  to the power of 16 to get the value of  a^{\frac{1}{2}}  -  Sufficient

Statement (2): Take  a^{\frac{1}{32}}  to the power of 64 to get the value of  a^{\frac{1}{2}}  -  Sufficient

If you look at it, both statements may have a different value for  a^{\frac{1}{2}} , but answer the question  independently . Hence the answer is (D).

GMATinsight · Answer

Question;  a^{\frac{1}{2}}  = ?

Statement 1 :  a^{\frac{1}{8}}=16

Taking 4th power both sides we get

(a^{\frac{1}{8}})^4=16^4

a^{\frac{1}{2}}=2^{16}

SUFFICIENT

Statement 2 :  a^{\frac{1}{32}}=2

Taking 16th power both sides we get

(a^{\frac{1}{32}})^{16}=2^{16}

a^{\frac{1}{2}}=2^{16}

SUFFICIENT

Answer: Option D

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

a is a positive number.
We have to find the value of  a^ {1/2} .

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:   a^{1/8}  = 16

The terms on both sides of the equation can be raised to the power of 4, since  \frac{1}{8}  * 4 = ½. 
Also,  16  =  2^4 .

a^{1/8}  =  2^4

Raising both sides to the power of 4, we have,

^4  =   ^4

By laws of exponents,   ^n  =  a^{mn}

Therefore,   ^4  =  a^{1/8 * 4}  =  a^{1/2}

And,   ^4  =  2^{4*4}  =  2^{16}

So,  a^{1/2}  =  2^{16}

The data in statement 1 is sufficient to find a unique value for  a^{1/2} 
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2:   a^{1/32}  = 2

The terms on both sides of the equation can be raised to the power of 16, since  \frac{1}{32}  * 16 = ½.

Also,  2  =  2^1 .

a^{1/32}  =  2^1

Raising both sides to the power of 16, we have,

^{16}  =   ^{16}

By laws of exponents,   ^n  =  a^{mn}

Therefore,   ^{16}  =  a^{1/32 * 16}  =  a^{1/2}

And,   ^{16}  =  2^{1*16}  =  2^{16}

So,  a^{1/2}  =  2^{16}

The data in statement 2 is sufficient to find a unique value for  a^{1/2} .
Statement 2 alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

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If a > 0, what is the value of a^(1/2)?

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