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3sqrt{0.6} (THE SIX HAS A REPEATING BAR OVER IT)

 May 6, 2021
 #1
avatar+363 
+1

0.6666=2/3

3sqrt(2/3)=sqrt6

 May 6, 2021
 #2
avatar+781 
+2

Let $x = 0.\overline{6}$

Thus, $10x = 6.\overline{6}$

Subtract these equations to get: $9x = 6.$

Thus, $x = 0.\overline{6} = \frac{2}{3}.$

We have $3 \sqrt{\frac{2}{3}} = 3 \frac{\sqrt{2}}{\sqrt{3}} = \frac{3 \sqrt{2}}{\sqrt{3}}.$

Then, if we multiply both the numerator and denominator by $\sqrt{3}$ we have 

$\frac{3 \sqrt{2} \sqrt{3}}{\sqrt{3} \sqrt{3}} = \frac{3 \sqrt{6}}{3} = \sqrt{6}$.

 

Thus, the answer is $\sqrt{6}$

 

laugh


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