What is $x \times \sqrt x$

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Does $x \times \sqrt x = x$?

I thought it was correct because sqrt is the opposite of multiplying by a number, so I figured by multiplying by a number it would balance out and be that number normally, but when I tried it with my Python calculator using 3 I got:

math.sqrt(3) * 3
5.196152422706632

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3 Answers

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In general, no. Since $\sqrt x$ is equal to $x^{1/2}$, your equation is the same as $x^{3/2} = x$, only $x = 0, 1$ work as solutions

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If you want to solve for the equation $$ x\sqrt{x} = x $$ then you have $$ x (\sqrt{x}-1) =0 \Rightarrow x = 0, \text{ or } \sqrt{x}=1, \text{ i.e. } x = 1 $$

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The multiplicative inverse (the "opposite" in your question) of a non-zero number $x$ is its reciprocal, $\frac{1}{x}$. Multiplying these two together gives instead $x \times \frac{1}{x} = 1$.

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