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What is the value of the expression 3 sqrt 80-2 sqrt 5
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24 May 2023, 05:48
24 May 2023, 05:48
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Question Stats:
82% (00:43) correct
17% (00:58) wrong based on 17 sessions
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What is the value of the expression \(3 \sqrt{80} - 2 \sqrt{5}\) ?
A. \(4 \sqrt{5}\)
B. \(5 \sqrt{3}\)
C. \(10 \sqrt{5}\)
D. \(12 \sqrt{3}\)
E. \(20 \sqrt{5}\)
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A. \(4 \sqrt{5}\)
B. \(5 \sqrt{3}\)
C. \(10 \sqrt{5}\)
D. \(12 \sqrt{3}\)
E. \(20 \sqrt{5}\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) Cracking the GRE Premium
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
Re: What is the value of the expression 3 sqrt 80-2 sqrt 5
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28 May 2023, 23:34
28 May 2023, 23:34
Expert Reply
OE
The problem is subtracting roots. Since roots cannot be subtracted unless the numbers under the radical sign are equal, look for a way to simplify the roots. Since 5 cannot be simplified any further, work with 80. The factors of 80 are 1 and 80, 2 and 40, 4 and 20, 5 and 16, and 8 and 10. Two of these pairs of factors contain a perfect square, but one contains a perfect square and a prime number. This is a good thing. This means that it could be reduced no further, so choose 5 and 16 and simplify to read
\(3 \sqrt{80}=3 \sqrt{5 *16} =3*4 \sqrt{5 }=12 \sqrt{5}\)
Now that the bases are equal, subtract the expression to find that \(12 \sqrt{5 }- 2 \sqrt{5}= 10 \sqrt{5}\)
The problem is subtracting roots. Since roots cannot be subtracted unless the numbers under the radical sign are equal, look for a way to simplify the roots. Since 5 cannot be simplified any further, work with 80. The factors of 80 are 1 and 80, 2 and 40, 4 and 20, 5 and 16, and 8 and 10. Two of these pairs of factors contain a perfect square, but one contains a perfect square and a prime number. This is a good thing. This means that it could be reduced no further, so choose 5 and 16 and simplify to read
\(3 \sqrt{80}=3 \sqrt{5 *16} =3*4 \sqrt{5 }=12 \sqrt{5}\)
Now that the bases are equal, subtract the expression to find that \(12 \sqrt{5 }- 2 \sqrt{5}= 10 \sqrt{5}\)
gmatclubot
Re: What is the value of the expression 3 sqrt 80-2 sqrt 5 [#permalink]
28 May 2023, 23:34
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