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

Write in the form ,\(a \sqrt b\) where a and b are positive integers:

 Jan 20, 2023
 #1
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1/sqrt(2) + 3/sqrt(8) + 6/sqrt(32)

= (1sqrt(2) + 3sqrt(2) + 6sqrt(2))/sqrt(2)

= 10sqrt(2)/sqrt(2)

= 10sqrt(2^1)

= 10sqrt(2)

 Jan 20, 2023
 #2
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\(\frac{1}{\sqrt2}+\frac{3}{\sqrt{8}}+\frac{6}{\sqrt{32}}\\\\ \frac{1}{\sqrt2}+\frac{3}{2\sqrt{2}}+\frac{6}{4\sqrt{2}}\\\\ \frac{1}{\sqrt2}(1+\frac{3}{2}+\frac{6}{4})\\\\ \frac{\sqrt2}{2}4\\\\ 2\sqrt2 \)

.
 Jan 22, 2023

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