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How would you simplify this? sqrt(52)*sqrt(48)+9*sqrt(52)

 Dec 31, 2015

Best Answer 

 #1
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+5

Simplify the following:
sqrt(52) sqrt(48)+9 sqrt(52)

sqrt(52)  =  sqrt(2^2×13)  =  2 sqrt(13):
2 sqrt(13) sqrt(48)+9 sqrt(52)

sqrt(48)  =  sqrt(2^4×3)  =  2^2 sqrt(3):
2 sqrt(13)×2^2 sqrt(3)+9 sqrt(52)

2^2 = 4:
2 sqrt(13)×4 sqrt(3)+9 sqrt(52)

sqrt(52)  =  sqrt(2^2×13)  =  2 sqrt(13):
2 sqrt(13)×4 sqrt(3)+9×2 sqrt(13)

2×4  =  8:
8 sqrt(13) sqrt(3)+9×2 sqrt(13)

sqrt(13) sqrt(3) = sqrt(13×3):
8 sqrt(13×3)+9×2 sqrt(13)

13×3  =  39:
8  sqrt(39 ) +9×2 sqrt(13)

9×2  =  18:
8 sqrt(39)+18 sqrt(13)

Factor 2 out of 8 sqrt(39)+18 sqrt(13) giving 2 (4 sqrt(39)+9 sqrt(13)):
Answer: | 2 (4 sqrt(39)+9 sqrt(13))

 Dec 31, 2015
 #1
avatar
+5
Best Answer

Simplify the following:
sqrt(52) sqrt(48)+9 sqrt(52)

sqrt(52)  =  sqrt(2^2×13)  =  2 sqrt(13):
2 sqrt(13) sqrt(48)+9 sqrt(52)

sqrt(48)  =  sqrt(2^4×3)  =  2^2 sqrt(3):
2 sqrt(13)×2^2 sqrt(3)+9 sqrt(52)

2^2 = 4:
2 sqrt(13)×4 sqrt(3)+9 sqrt(52)

sqrt(52)  =  sqrt(2^2×13)  =  2 sqrt(13):
2 sqrt(13)×4 sqrt(3)+9×2 sqrt(13)

2×4  =  8:
8 sqrt(13) sqrt(3)+9×2 sqrt(13)

sqrt(13) sqrt(3) = sqrt(13×3):
8 sqrt(13×3)+9×2 sqrt(13)

13×3  =  39:
8  sqrt(39 ) +9×2 sqrt(13)

9×2  =  18:
8 sqrt(39)+18 sqrt(13)

Factor 2 out of 8 sqrt(39)+18 sqrt(13) giving 2 (4 sqrt(39)+9 sqrt(13)):
Answer: | 2 (4 sqrt(39)+9 sqrt(13))

Guest Dec 31, 2015
 #2
avatar+118587 
+5

Hi guests :)

How would you simplify this? sqrt(52)*sqrt(48)+9*sqrt(52)

 

\(\sqrt{52}*\sqrt{48}+9*\sqrt{52}\\ = \sqrt{4*13}*\sqrt{16*3}+9*\sqrt{4*13}\\ = 2\sqrt{13}*4\sqrt{3}+9*2\sqrt{13}\\ = 8\sqrt{39}\qquad\;\;\;+18\sqrt{13}\\\)

 

Exactly as guest already said :)

 Dec 31, 2015
edited by Melody  Dec 31, 2015

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