If m 0 and n 0, which of the following is equivalent to

Question

If m > 0 and n > 0, which of the following is equivalent to  \frac{mn}{m^2}*\sqrt{\frac{m^2}{n}} ?

A.  \sqrt{n}

B.  \frac{nm}{\sqrt{n}}

C.  \frac{m^2}{n}

D.  \frac{n^2}{m}

E.  \frac{1}{mn}

mariaraashidkoul · Answer

This is a pretty easy one. Just simply multiply what's given in the question which leads to m^2*n/m^2*{sqrt }. m^2 will get cancelled and we will be left with n/sqrt . Multiply both numerator and denominator by sqrt  which gives n*sqrt /{sqrt }^2 = sqrt

FarahE · Answer

Can someone help and let me know what am I doing wrong?

I solved it as follows:

mn/m^2 *  (m^2/n)

= n/m *  (m^2/n)

= n/m * m/ n

= n*m/m* n

=n/ n

Chibvike · Answer

Honestly, I got this same final answer but guessed option A because I read that the GMAT does not like radicals as denominators

It'll be helpful for someone to explain what was wrong in this process

Bunuel · Answer

Nothing wrong. But we don't have  \frac{n}{\sqrt{n}}  among the answer choices. However, if you rationalize the fraction you get:
 
 \frac{n}{\sqrt{n}}=

=\frac{n*\sqrt{n}}{\sqrt{n}*\sqrt{n}}=

=\frac{n*\sqrt{n}}{n}=

=\sqrt{n} .
 
Which is option A.

Hope it's clear.

StenAnsiktet · Answer

I do not understand the steps of simplification here and what exponent rules are used.

I understand the first step mn/m^2=n/m but I am lost here:
= n/m *  (m^2/n)

= n/m * m/ n

= n*m/m* n

Could someone please elaborate and explain? Thanks!

Bunuel · Answer

If m > 0 and n > 0, which of the following is equivalent to  \frac{mn}{m^2}*\sqrt{\frac{m^2}{n}} ?

A.  \sqrt{n}

B.  \frac{nm}{\sqrt{n}}

C.  \frac{m^2}{n}

D.  \frac{n^2}{m}

E.  \frac{1}{mn}

\frac{mn}{m^2}*\sqrt{\frac{m^2}{n}}=

=\frac{n}{m}*\frac{|m|}{ \sqrt {n}}=

Since m > 0, then |m| = m and we have:

=\frac{n}{m}*\frac{m}{ \sqrt {n}}= 
 
  =n*\frac{1}{ \sqrt {n}}= 
 
  =\frac{n}{ \sqrt {n}}

Rationalize the fraction by multiplying both numerator and denominator by  \sqrt{n} :

\frac{n}{\sqrt{n}}=

=\frac{n*\sqrt{n}}{\sqrt{n}*\sqrt{n}}=

=\frac{n*\sqrt{n}}{n}=

=\sqrt{n} .

Answer: A.

Hope it's clear.

StenAnsiktet · Answer

Thank you so much  Bunuel  that's very helpful, all clear now!

If m > 0 and n > 0, which of the following is equivalent to

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