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# ​ What is the simplest form of the radical expression 48x4y3−−−−−√ ?

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What is the simplest form of the radical expression 48x4y3−−−−−−√ ?

Mar 1, 2018

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$$\quad\sqrt{48x^4y^3} \\ =\\ \quad\sqrt{2\cdot2\cdot2\cdot2\cdot3\cdot x^4\cdot y^3} \\ =\\ \quad\sqrt{2^4\cdot3\cdot x^4\cdot y^3} \\ =\\ \quad\sqrt{2^4\cdot3\cdot x^4\cdot y^2\cdot y} \\ =\\ \quad\sqrt{2^4\cdot x^4\cdot y^2\cdot 3\cdot y} \\ =$$

$$\quad\sqrt{2^4}\cdot \sqrt{x^4}\cdot \sqrt{y^2}\cdot \sqrt{3\cdot y}\\ =\\ \quad2^2\cdot x^2\cdot y\cdot\sqrt{3\cdot y}\\ =\\ \quad4x^2y\sqrt{3 y}$$          Since  x  and  y  are positive, we can say...

Mar 4, 2018
edited by hectictar  Mar 4, 2018