+0  
 
0
53
2
avatar

 

 

Write in the form , where  and  are positive integers:

\[\frac{1}{\sqrt{2}} +\frac{3}{\sqrt{8}} + \frac{6}{\sqrt{32}}.\]

 Dec 21, 2021
 #1
avatar
0

This works out to 3*sqrt(2).

 Dec 21, 2021
 #2
avatar+22583 
+1

Multiplying each term by  sqrt(2) / sqrt(2)

 

1/sqrt(2)  +  3/sqrt(8)  + 6/sqrt(32)

 

=  sqrt(2) / sqrt(4)  +  3sqrt(2) / sqrt(16)  +  6sqrt(2)/sqrt(64)

 

=  sqrt(2) / 2  +  3sqrt(2) / 4  +  6sqrt(2) / 8                     

 

=  2sqrt(2) / 4  +  3sqrt(2) / 4  + 3sqrt(2) / 4               (writing each fraction with a denominator of 4)

 

=  8sqrt(2) / 4

 

=  2sqrt(2)

 Dec 21, 2021

8 Online Users

avatar