If m and n are both positive, what is the value of m*root(n)

for this problem:

m^2*n=100
m^2=100\n
m=sqrt(100\n)

since no number is -ve when sqrt the answer is d

If m and n are both positive, what is the value of \(m*\sqrt{n}\)?

(1) \(\frac{m*n}{\sqrt{n}}=10\)

(2) \(\frac{m^2*n}{2}=50\)

The textbook answer says (D) but the Square root of choice (2) will give us +/- 10.
Should we ignore -10 and conclude that (2) also gives us the answer

Bunuel ,
If they had not provided that m and n both are positive then also statement B alone would be sufficient right ??
I mean when question stem itself provides sqaure root sign , we should consider only POSITIVE root right ??

Hi,
the answer in that case will not B..
statement two will give you two values for m one +ive and other -ive..

Please help clarify my doubt for statement 2.it says that m^2n=2*50
So basically,m^2*n=100,wherein there can be three possibilities
10^2 *1=100
5^2 *4=100,or
2^2 *25=100
Then how can we determine that it is the first scenario only??? please correct my concept if I am wrong

The question asks to find the value of \(m*\sqrt{n}\). In all cases you consider there the value of \(m*\sqrt{n}\) is the same: 10.

(1) \(\frac{m*n}{\sqrt{n}}=10\)

Multiply both numerator and denominator by \sqrt{n}

we will get \(m*\sqrt{n}\)= 10

(2) \(\frac{m^2*n}{2}=50\)

\frac{m^2*n}{2}= 100
Squaring both sides \(m*\sqrt{n}\)= 10

D is the answer

1) msqrt(n) = 10
2) m2n = 100
square root on both sides
msqrt(n) = 10
Answer :D

I missed a simple mistake, if anyone can clarify the procedure for step 1, I would appreciate it.

as follows:

1) m * n / Sq.rt (n) = 10
2) Sq. rt (n) / Sq. rt (n) * m * n / Sq.rt (n) - step is rationalizing the denominator
3) m * n * Sq. rt (n) / n = 10
4) m * sq.rt (n) = 10 the n from the denominator and numerator cancel
5) result m * Sq.rt (n) = 10, so sufficient

Hello Kapstone,
I don’t think there’s anything wrong at all with your approach. If anything, it’s as comprehensive as it can be.

The only thing I would have changed about your approach is the fact that you rationalized the denominator. If you have an ‘n’ in the numerator and a '√n' in the denominator, express n as the product of √n and √n i.e. n = √n * √n. Cancel out the √n from the numerator and the denominator, this will leave you with a √n in the numerator.
This will reduce time and the number of steps.

Rationalising the denominator is advisable when you have a more complex surd (root) like say 2+√3, wherein you multiply and divide the given expression with the conjugate of the surd and simplify using the (a-b)(a+b) = \(a^2\) - \(b^2\) identity.

So, there was nothing wrong with your analysis of Statement I (not step I) at all; it’s just that you could have followed a simpler approach of simplifying the given expression.
Hope that helps!

Thanks!

That makes a lot of sense.

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