a) \(\sqrt{27x^2}\)
\(=\sqrt{3^2\cdot3x^2}\)
\(=\left|3x\right|\sqrt{3}\)
\(=3\left|x\right|\sqrt{3}\)
b) \(\sqrt{8xy^2}\)
\(=\sqrt{2^2\cdot2\cdot x\cdot y^2}\)
\(=\left|2y\right|\sqrt{2x}\)
\(=2\left|y\right|\sqrt{2x}\)
c) \(\sqrt{25x^3}\)
\(=\sqrt{5^2\cdot x^2\cdot x}\)
\(=\left|5x\right|\sqrt{x}\)
\(=5\left|x\right|\sqrt{x}\)
d) \(\sqrt{48xy^4}\)
\(=\sqrt{4^2\cdot3x\cdot\left(y^2\right)^2}\)
\(=\left|4y^2\right|\sqrt{3x}\)
\(=4y^2\sqrt{3x}\)
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`a, sqrt(27x^2b) = sqrt(3^2. 3.x^2b) = 3|x|sqrt(3b)`.
`b, sqrt(8xy^2) =sqrt(2^2.2xy^2)= 2|y|sqrt(2x)`
`c, sqrt(25x^3d) = sqrt(5^2.x^2.x.d) = 5|x|sqrt(xd)`.
`d, sqrt(48xy^4) = sqrt(4^2.3 . xy^4) = 4y^2sqrt(3x)`.
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