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555-605 (Medium)|   Roots|      
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BrentGMATPrepNow
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Which of the following is closest to [m][fraction]{[square_root]150[/s 08 Nov 2018, 12:10
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74% (01:43) correct 26% (02:37) wrong based on 448 sessions

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Which of the following is closest to \(\frac{(\sqrt{150})(\sqrt{405})}{\sqrt{105}-\sqrt{50}}\)?

A) 10
B) 20
C) 40
D) 80
E) 120
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D
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Which of the following is closest to [m][fraction]{[square_root]150[/s 08 Nov 2018, 13:02
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Sqrt(105) is approx 10.
Sqrt(405) is approx 20.
Sqrt(150) is approx 12.
Sqrt(50) is approx 7.

Now substituting this,

12*20/10-7 = 4*20 = 80.

D is the answer

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Which of the following is closest to [m][fraction]{[square_root]150[/s 27 Oct 2022, 01:12
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BrentGMATPrepNow
Which of the following is closest to \(\frac{(\sqrt{150})(\sqrt{405})}{\sqrt{105}-\sqrt{50}}\)?

A) 10
B) 20
C) 40
D) 80
E) 120
Show more

Hi BrentGMATPrepNow, I approximate it as \(\frac{(\sqrt{100 + 50})(\sqrt{400 + 5})}{\sqrt{100 + 5}-\sqrt{50}}\)
So I get (10 + 7) (20 * square_root 5 / 10 * square_root 5 - 7
17 * 20 * square_root 5 / 10 square_root 5 - 7 and get answer 113.3
What went wrong here? Could you advise? Thanks Brent
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Which of the following is closest to [m][fraction]{[square_root]150[/s 27 Oct 2022, 06:57
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Kimberly77
BrentGMATPrepNow
Which of the following is closest to \(\frac{(\sqrt{150})(\sqrt{405})}{\sqrt{105}-\sqrt{50}}\)?

A) 10
B) 20
C) 40
D) 80
E) 120

Hi BrentGMATPrepNow, I approximate it as \(\frac{(\sqrt{100 + 50})(\sqrt{400 + 5})}{\sqrt{100 + 5}-\sqrt{50}}\)
So I get (10 + 7) (20 * square_root 5 / 10 * square_root 5 - 7
17 * 20 * square_root 5 / 10 square_root 5 - 7 and get answer 113.3
What went wrong here? Could you advise? Thanks Brent
Show more

Hi Kimberly,

You are using a square root property that doesn't exist.
That is, there's no square root property that says \(\sqrt{x+y} = \sqrt{x} + \sqrt{y}\)

Tip: If you're not entirely sure whether a property is true, you can always test numbers.
For example \(\sqrt{4}\) can be written as \(\sqrt{1+1+1+1}\)
If we apply your faulty property we get, \(\sqrt{1+1+1+1} = \sqrt{1} + \sqrt{1} + \sqrt{1} + \sqrt{1} = 1+1+1+1 = 4\)
So, by applying your property we get \(\sqrt{4} = 4\), which is not true, which means the property can't be true.
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Which of the following is closest to [m][fraction]{[square_root]150[/s 27 Oct 2022, 14:03
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Great explanation always and crystal clear now thanks BrentGMATPrepNow
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Which of the following is closest to [m][fraction]{[square_root]150[/s 27 Feb 2024, 07:40
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rt(150)=12.7, rt(405)=20
rt(105)=10, rt(50)=7

12.5 x 20/3
=12.5x6=75 (approx)

80)
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Which of the following is closest to [m][fraction]{[square_root]150[/s 22 Mar 2025, 10:55
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Can someone solve this without approximation I'm dtuck
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Which of the following is closest to [m][fraction]{[square_root]150[/s 23 Mar 2025, 02:03
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BrentGMATPrepNow
Which of the following is closest to \(\frac{(\sqrt{150})(\sqrt{405})}{\sqrt{105}-\sqrt{50}}\)?

A) 10
B) 20
C) 40
D) 80
E) 120

Can someone solve this without approximation I'm dtuck
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The expression results in an irrational number, so you’ll have to approximate at some point - there’s no way to get an exact integer value without estimation.
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