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Math Expert V
Joined: 02 Sep 2009
Posts: 58060
What is 63^(1/2)/147^(1/2)  [#permalink]

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Difficulty:   15% (low)

Question Stats: 73% (01:47) correct 27% (01:33) wrong based on 195 sessions

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What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\frac{3}{7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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2
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\sqrt{63} = 3\sqrt{7}$$
$$\sqrt{147} = 7\sqrt{3}$$

So, $$\frac{\sqrt{63}}{\sqrt{147}}$$

$$= 3\sqrt{7}/7\sqrt{3}$$

$$= 3\sqrt{7}*\sqrt{3}/7\sqrt{3}*\sqrt{3}$$

= $$3\sqrt{21}/7*3$$

= $$\frac{\sqrt{21}}{7}$$

Thus, answer will be (C)
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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1
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

Bunuel Option B and C are the same

B) √(3/7)
C) √21/7 = √3*√7/√7*√7= √(3/7)
.

Posted from my mobile device
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\frac{\sqrt{63}}{\sqrt{147}}$$

$$\sqrt{7*3*3/7*7*3}$$

$$\sqrt{3/7}$$ . Answer (B)...
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\frac{\sqrt{63}}{\sqrt{147}}$$
=$$\frac{\sqrt{3*3*7}}{\sqrt{3*7*7}}$$
=$$\frac{\sqrt{3}}{\sqrt{7}}$$

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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Why the answer isn't C?

I divide both Numerator and Denominator by 3 and I get 21/49 under square root
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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+C

we must not leave square roots in denominator.
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What is 63^(1/2)/147^(1/2)  [#permalink]

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What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

$$\frac{\sqrt{63}}{\sqrt{147}}$$

$$\frac{\sqrt{7 * 3 * 3}}{\sqrt{7 * 7 *3}}$$

$$\frac{3 * \sqrt{7}}{7 * \sqrt{3}}$$

$$\frac{3 * \sqrt{7} * \sqrt{3}}{7 * \sqrt{3} * \sqrt{3}}$$

$$\frac{3 * \sqrt{21}}{7 * 3}$$

$$\frac{\sqrt{21}}{7}$$

Hence, Answer is C
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Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Originally posted by ydmuley on 26 Jun 2017, 11:37.
Last edited by ydmuley on 26 Jun 2017, 12:40, edited 1 time in total.
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Abhishek009 wrote:
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\sqrt{63} = 3\sqrt{7}$$
$$\sqrt{147} = 7\sqrt{3}$$

So, $$\frac{\sqrt{63}}{\sqrt{147}}$$

$$= 3\sqrt{7}/7\sqrt{3}$$

$$= 3\sqrt{7}*\sqrt{3}/7\sqrt{3}*\sqrt{3}$$

= $$3\sqrt{21}/7*3$$

= $$\frac{\sqrt{21}}{7}$$

Thus, answer will be (C)

Hello Abhishek009 - Why not B in this case? Are you referring to any specific rule to solve this question?
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"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Math Expert V
Joined: 02 Sep 2009
Posts: 58060
Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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GMATinsight wrote:
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

Bunuel Option B and C are the same

B) √(3/7)
C) √21/7 = √3*√7/√7*√7= √(3/7)
.

Posted from my mobile device

Yes, formatting error there. B is simply $$\frac{3}{7}$$, not $$\sqrt{3/7}$$. Edited. Thank you.
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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ydmuley wrote:
Abhishek009 wrote:
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\sqrt{63} = 3\sqrt{7}$$
$$\sqrt{147} = 7\sqrt{3}$$

So, $$\frac{\sqrt{63}}{\sqrt{147}}$$

$$= 3\sqrt{7}/7\sqrt{3}$$

$$= 3\sqrt{7}*\sqrt{3}/7\sqrt{3}*\sqrt{3}$$

= $$3\sqrt{21}/7*3$$

= $$\frac{\sqrt{21}}{7}$$

Thus, answer will be (C)

Hello Abhishek009 - Why not B in this case? Are you referring to any specific rule to solve this question?

You can ignore this as Bunuel has changed the options.
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"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
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GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\frac{3}{7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

To resolve the confusion earlier in the thread, here's a recap:

- Originally, B incorrectly said $$\sqrt{\frac{3}{7}}$$
- This is actually the same as C, just simplified differently. $$\sqrt{\frac{3}{7}}$$ and $$\frac{\sqrt{21}}{7}$$ have the same value - you can plug them into a calculator to check.  - The GMAT will never do this. If the answer choices are numbers, the right answer will always be the one and only answer that has the correct value. You'll never have to make a decision based on how the answer is formatted.
- Unfortunately, that means you can't eliminate answer choices just because they have a square root in the denominator (for example!).
- However, look out for situations where you simplify the answer in a certain way, and then you don't see that answer choice in the options - especially in problems that have square roots and exponents. Normally, you might assume that you got the wrong answer. However, it's possible that your answer is in the answer choices, but it's just written differently. Look out for that!
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\frac{3}{7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\frac{\sqrt{63}}{\sqrt{147}}$$

$$\sqrt{3^2 * 7} / \sqrt{7^2 * 3}$$

$$3 \sqrt{7}/7\sqrt{3}$$

Multiplying numerator and denominator with $$\sqrt{3}$$

$$3 \sqrt{7} * \sqrt{3}$$$$/ 7 * \sqrt{3}$$ * $$\sqrt{3}$$

$$3 \sqrt{21} / 7 * 3$$

$$\sqrt{21}/7$$ . Answer (C)...
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\frac{3}{7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

√63/√147 < 8/12 = 0.64

A) √3/7 = 1.7/7= 0.2
B) (3/7) = 0.43
C) √21/7 = 4.6/7= 0.65
D) 3√21/7 = 1.8
E) 7/√3 = 4.1

I always prefer approximation in all such questions...

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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\frac{3}{7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$
'

We can simplify the given expression:

√63/√147 = (√9 x √7)/(√49 x √3) = (3√7)/(7√3)

Multiplying by √3/√3, we have:

(3√21)/21 = √21/7

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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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sashiim20 wrote:
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\frac{\sqrt{63}}{\sqrt{147}}$$

$$\sqrt{7*3*3/7*7*3}$$

$$\sqrt{3/7}$$ . Answer (B)...

Both B & C are correct. But now the option B has changed from $$\sqrt{3/7}$$ to $$3/7$$. So, wrt to current question, (C) is correct.
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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Abhishek009 wrote:
Bunuel wrote:
What is $$\frac{\sqrt{63}}{\sqrt{147}}$$?

A. $$\frac{\sqrt{3}}{7}$$

B. $$\sqrt{3/7}$$

C. $$\frac{\sqrt{21}}{7}$$

D. $$\frac{3\sqrt{21}}{7}$$

E. $$\frac{7}{\sqrt{3}}$$

$$\sqrt{63} = 3\sqrt{7}$$

$$\sqrt{147} = 7\sqrt{3}$$

So, $$\frac{\sqrt{63}}{\sqrt{147}}$$

$$= 3\sqrt{7}/7\sqrt{3}$$

$$= 3\sqrt{7}*\sqrt{3}/7\sqrt{3}*\sqrt{3}$$

= $$3\sqrt{21}/7*3$$

= $$\frac{\sqrt{21}}{7}$$

Thus, answer will be (C)

Both B & C are correct. But now the option B has changed from $$\sqrt{3/7}$$ to $$3/7$$. So, wrt to current question, (C) is correct.
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Re: What is 63^(1/2)/147^(1/2)  [#permalink]

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