Which of the following is closest to [m][fraction]{[square_root]150[/s

Question

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

Chethan92 · Accepted Answer

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

Posted from my mobile device

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

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.

Kimberly77 · Answer

Great explanation always and crystal clear now thanks  BrentGMATPrepNow

Oppenheimer1945 · Answer

rt(150)=12.7, rt(405)=20
rt(105)=10, rt(50)=7

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

80)

kayarat600 · Answer

Can someone solve this without approximation I'm dtuck

Bunuel · Answer

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.

Which of the following is closest to [m][fraction]{[square_root]150[/s

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Which of the following is closest to [m][fraction]{[square_root]150[/s

Prep Toolkit

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