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avatar+675 

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
avatar+7545 
+3

\(x^a\cdot x^b\,=\,x^{a+b}\)

 

So....

 

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

 

smiley

 Apr 6, 2018
 #2
avatar+675 
+2

well done B)

thejamesmachine  Apr 6, 2018

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