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# Square root of 7 + square root 48

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Senior Manager
Joined: 05 Oct 2008
Posts: 258
Square root of 7 + square root 48 [#permalink]

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06 Nov 2008, 03:18
$$\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?$$

# 1.0
# 1.7
# 2.0
# 2.4
# 3.0

Can you please provide the full solution. Thanks

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VP
Joined: 17 Jun 2008
Posts: 1479

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06 Nov 2008, 03:37
study wrote:
$$\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?$$

# 1.0
# 1.7
# 2.0
# 2.4
# 3.0

Can you please provide the full solution. Thanks

Say $$\sqrt{7 + \sqrt{48}} - \sqrt{3} = x$$
or, $$\sqrt{7 + \sqrt{48}} = x + \sqrt{3}$$
squaring both sides,
$$7 + 4\sqrt{3} = x^2 + 2x\sqrt{3} + 3$$
or, $$4 + 4\sqrt{3} = x(x + 2\sqrt{3})$$
or $$2(2 + 2\sqrt{3} = x(x + 2\sqrt{3})$$

Hence, x = 2.

I am sure there would be an easier way out.
Manager
Joined: 23 Aug 2008
Posts: 62

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06 Nov 2008, 03:48
study wrote:
$$\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?$$

# 1.0
# 1.7
# 2.0
# 2.4
# 3.0

Can you please provide the full solution. Thanks

I'm going for 2.0, but in an unorthodox way compared to scthakur...

$$\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?$$
This is approx = $$\sqrt{14} - \sqrt{3}$$ since $$\sqrt{49}=7$$
$$\sqrt{14}$$ is between 3 and 4 (closer to 4), since $$\sqrt{9} < \sqrt{14} < \sqrt{16}$$

Then plugging in the answers (knowing $$\sqrt{3}$$ approx = 1.7)
1.7 + 3.0 = 4.7 = too high (above 4)
1.7 + 2.4 = 4.1 = too high (above 4)
1.7 + 2.0 = 3.7 = about right
1.7 + 1.7 = 3.4 = clearly too low (since $$\sqrt{14} > \sqrt{3} , and \sqrt{3}=1.7$$)

I found this method quite quick (~1 minute), although I do appreciate the algebraic method.
Manager
Joined: 30 Sep 2008
Posts: 111

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06 Nov 2008, 04:26
for this type of question, usually the function under the square root is a square.

$$7+sqrt(48) = 7 + 4*sqrt(3) = 3 + 2*2*sqrt(3) + 2^2 = (sqrt(3) + 2)^2$$
Director
Joined: 14 Aug 2007
Posts: 695

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06 Nov 2008, 05:56
lylya4 wrote:
for this type of question, usually the function under the square root is a square.

$$7+sqrt(48) = 7 + 4*sqrt(3) = 3 + 2*2*sqrt(3) + 2^2 = (sqrt(3) + 2)^2$$

Nice approach!

Though I will consider it safe to use algebraic method on the D day

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Square Roots   [#permalink] 06 Nov 2008, 05:56
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# Square root of 7 + square root 48

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