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[Drum_2014]

How do you simplify sqrt of 2/3

 

[tkhunny]

How would you like to simplify it? That's about as simple as you can get, but some folks get nausea and headaches when they see a radical in a denominator.

\(\displaystyle \sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} = \frac{\sqrt{2}}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{2}\cdot \sqrt{3}}{\sqrt{2}\cdot \sqrt{3}} = \frac{\sqrt{2\cdot 3}}{\sqrt{3\cdot 3}}\)

Can you finish?

I still think this final result is no more simplified than where we started, but I tend to be in a minority on this discussion.

 

[soroban]

Hello, Drum_2014!

Another approach . . .

\(\displaystyle \text{Simplify: }\,\sqrt{\dfrac{2}{3}}\)

Multiply the fraction by \(\displaystyle \frac{3}{3}\)

. . \(\displaystyle \sqrt{\dfrac{2}{3}\cdot\dfrac{3}{3}} \;=\; \sqrt{\dfrac{6}{9}} \;=\;\dfrac{\sqrt{6}}{\sqrt{9}} \;=\;\dfrac{\sqrt{6}}{3} \)