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Simplify the expression 1/sqrt(2) + 3/sqrt(8) + 5/sqrt(32).

 Jan 31, 2022
 #1
avatar+1209 
+3

\(\frac{1}{\sqrt{2}} + \frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}\)

\(= \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} + \frac{3}{2\sqrt{2}} + \frac{5}{4\sqrt{2}}\)

\(= \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{3}{2 \sqrt{2}} + \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{5}{4\sqrt{2}}\)

\(= \frac{\sqrt{2}}{2} + \frac{3 \sqrt{2}}{4} + \frac{5 \sqrt{2}}{8}\)

\(= \frac{4 \sqrt{2} + 6\sqrt{2} + 5\sqrt{2}}{8}\)

\(=\boxed{\frac{15\sqrt{2}}{8}}\)

.
 Jan 31, 2022
 #2
avatar+360 
+3

\(\frac{1}{\sqrt{2}}+\frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}\)

\(\frac{1}{\sqrt{2}}+\frac{3}{2\sqrt{2}}+\frac{5}{4\sqrt{2}} \)

\(\frac{4}{4\sqrt{2}}+\frac{6}{4\sqrt{2}}+\frac{5}{4\sqrt{2}}\)

\(\frac{15}{4\sqrt{2}}\)

hmm........ we got different answers

 Jan 31, 2022
 #3
avatar+1209 
+2

These answers are equivalent, as shown below:

 

\(\frac{15}{4 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \boxed{\frac{15\sqrt{2}}{8}}\)

 

This process is called rationalizing the denominator.

CubeyThePenguin  Jan 31, 2022
 #4
avatar+360 
+4

totally forgot alll about that lol

thanks you for reminding me!

 Feb 2, 2022

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