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Simplify:

\(\dfrac{\sqrt{338}}{\sqrt{288}}+\dfrac{\sqrt{150}}{\sqrt{96}}\)

Express your answer as a common fraction.

 Aug 16, 2019
 #1
avatar+103122 
+1

√338      √ 150

____  +  _____    =

√288         √96

 

13√2         5√6

____  +    ____   =

12√2         4√6

 

13             5

__    +      __   =

12             4

 

13         15

__  +     ___     =

12         12

 

28

__    =

12

 

7

__

3

 

 

 

cool cool cool

 Aug 16, 2019
 #2
avatar+93 
+2

Hi Guest, 

First, 

\(\frac{\sqrt{338}}{\sqrt{288}}+\frac{\sqrt{150}}{\sqrt{96}} = \frac{13}{2^2\cdot \:3}+\frac{\sqrt{150}}{\sqrt{96}}\)

 

Next, \(\frac{13}{2^2\cdot \:3}+\frac{\sqrt{150}}{\sqrt{96}} = \frac{13}{2^2\cdot \:3}+\frac{5}{2^2}\)

 

Simplifying again, \(\frac{13}{2^2\cdot \:3}+\frac{5}{2^2} = \frac{13}{12}+\frac{5}{2^2}\)

 

Lastly, \(\frac{13}{12}+\frac{5}{2^2} = \frac{13}{12} + \frac{5}{4} = \frac{13}{12}+\frac{15}{12} = \frac{28}{12} = \frac{7}{3}\)

 

Your welcome :P, Evancool

 Aug 16, 2019
 #3
avatar+93 
+2

Oops CPhill was more detailed Sorry!blush

 Aug 16, 2019

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