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

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



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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,

\([a^{1/8}]^4\) = \([2^4]^4\)

By laws of exponents, \([a^m]^n\) = \(a^{mn}\)

Therefore, \([a^{1/8}]^4\) = \(a^{1/8 * 4}\) = \(a^{1/2}\)

And, \([2^4]^4\) = \(2^{4*4}\) = \(2^{16}\)

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,

\([a^{1/32}]^{16}\) = \([2^1]^{16}\)

By laws of exponents, \([a^m]^n\) = \(a^{mn}\)

Therefore, \([a^{1/32}]^{16}\) = \(a^{1/32 * 16}\) = \(a^{1/2}\)

And, \([2^1]^{16}\) = \(2^{1*16}\) = \(2^{16}\)

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.