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# Brain Teaser

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What is the square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power?

Apr 6, 2018

#1
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$$x^a\cdot x^b\,=\,x^{a+b}$$

So....

$$\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}\,=\,\sqrt3^{\sqrt2+-\sqrt2}\\~\\ \phantom{\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}}\,=\,\sqrt3^{\sqrt2-\sqrt2}\\~\\ \phantom{\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}}\,=\,\sqrt3^0\\~\\ \phantom{\sqrt3^\sqrt2\cdot\sqrt3^{-\sqrt2}}\,=\,1$$

Apr 6, 2018
#2
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well done B)

thejamesmachine  Apr 6, 2018