a) \(-\dfrac{2}{3}\sqrt{xy}\)
\(=-\sqrt{\left(\dfrac{2}{3}\right)^2xy}\)
\(=-\sqrt{\dfrac{4}{9}xy}\)
b) \(x\sqrt{5}\)
\(=\sqrt{x^2\cdot5}\)
\(=\sqrt{5x^2}\)
c) \(x\sqrt{13}\)
\(=-\sqrt{13\cdot x^2}\)
\(=-\sqrt[]{13x^2}\)
d) \(x\sqrt{\dfrac{2}{x}}\)
\(=\sqrt{x^2\cdot\dfrac{2}{x}}\)
\(=\sqrt{2x}\)
e) \(a\sqrt{13}\)
\(=\sqrt{13\cdot a^2}\)
\(=\sqrt{13a^2}\)
f) \(a\sqrt{\dfrac{-15}{a}}\)
\(=-\sqrt{\dfrac{-15}{a}\cdot a^2}\)
\(=-\sqrt{-15a}\)
g) \(\dfrac{a}{2}\sqrt{\dfrac{12}{a}}\)
\(=\sqrt{\dfrac{a^2}{4}\cdot\dfrac{12}{a}}\)
\(=\sqrt{3a}\)
h) \(a\sqrt{2}\)
\(=-\sqrt{2a^2}\)
5:
a: \(=\sqrt{\dfrac{2a}{3}\cdot\dfrac{3a}{8}}=\sqrt{\dfrac{a^2}{4}}=\dfrac{a}{2}\)
b: \(=\sqrt{13a\cdot\dfrac{52}{a}}=\sqrt{13\cdot52}=13\cdot2=26\)
c: \(=2y^2\cdot\dfrac{x^2}{-2y}=-x^2y\)
d: \(=ab^2\cdot\dfrac{\sqrt{3}}{-ab^2}=-\sqrt{3}\)
g: \(=5xy\cdot\dfrac{-5x}{y^3}=-\dfrac{25x^2}{y^2}\)
