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lara31 [8.8K]
4 years ago
7

Simplify w/ positive values

Mathematics
1 answer:
Licemer1 [7]4 years ago
6 0
\bf \sqrt{\cfrac{3x^5}{75x^9}}\qquad 
\begin{cases}
75=3\cdot 5\cdot 5\to 3\cdot 5^2\\
x^9\to x^{5+4}\to x^5\cdot x^4
\end{cases}\qquad thus
\\\\\\\\
\sqrt{\cfrac{3x^5}{3\cdot 5^2\cdot x^5\cdot x^4}}\implies \sqrt{\cfrac{3x^5}{3x^5}\cdot \cfrac{1}{5^2x^4}}\implies \sqrt{1\cdot \cfrac{1}{5^2x^4}}
\\\\\\\\
\sqrt{\cfrac{1}{5^2x^4}}\qquad 
\begin{cases}
1^2\to 1\\
x^4\to x^{2\cdot 2}\to (x^2)^2
\end{cases}\qquad thus
\\\\


\bf \sqrt{\cfrac{1}{5^2x^4}}\implies \sqrt{\cfrac{1^2}{5^2(x^2)^2}}\implies \sqrt{\cfrac{1^2}{(5x^2)^2}}\implies \sqrt{\left( \cfrac{1}{5x^2} \right)^2}
\\\\\\
\cfrac{1}{5x^2}
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