If a 0 and a/b = b^(1/2), what is b in terms of a?

Question

If a > 0 and  \frac{a}{b} = \sqrt{b} , what is b in terms of a?

A. 1/a
B.  \sqrt{a} 
C.  a\sqrt{a} 
D. a^(2/3)
E. a^3 - a^2

Mohammadmo · Answer

a^2 /b^2 =b
b^3=a^2
b=a^ 2/3
Option D

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BrentGMATPrepNow · Answer

Useful concept: If  k ≥ 0 , then  (\sqrt{k})^2=k

Given:  \frac{a}{b} = \sqrt{b}

Square both sides to get:  (\frac{a}{b})^2 = (\sqrt{b})^2

Simplify:  \frac{a^2}{b^2} = b

Multiply both sides by  b^2  to get:  a^2 = b^3

Raise both sides to the power of  \frac{1}{3}  to get:  (a^2)^{\frac{1}{3}} = (b^3)^{\frac{1}{3}}

Applied the Power of a Power rule to get:  a^{\frac{2}{3}} = b

Answer: D

Cheers,
Brent

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • The number a > 0 and a/b = √b

To find  
We need to determine
 • The value of b, in terms of a

Approach and Working out  
From the given expression, we can simplify it further and write it as:
 • a/b = √b
Or, a = b√b
Or,  a^2 = b^2 * b = b^3 
Or,  b^3 = a^2 
Or,  b = a^{2/3}

Thus, option D is the correct answer.

Correct Answer: Option D

hiranmay · Answer

If a > 0 and  \frac{a}{b} = \sqrt{b} , what is b in terms of a?

A. 1/a
B.  \sqrt{a} 
C.  a\sqrt{a} 
D. a^(2/3) -->   correct :  \frac{a}{b} = \sqrt{b}  =>  a = b* \sqrt{b}  = b^(3/2) => b = a^(2/3) 
E. a^3 - a^2

ScottTargetTestPrep · Answer

Squaring both sides, we have:

a^2/b^2 = b

a^2 = b^3

a^(⅔) = b

Answer: D

If a > 0 and a/b = b^(1/2), what is b in terms of a?

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