Question

Rút gọn:

a. \(\sqrt{2a}\) \(\times\) \(\sqrt{18a}\) _{(a \(\ge\)0)}

_{b. \(\sqrt{3a\times27ab^2}\)}

c. 2y^{2 \(\times\) \(\sqrt{\dfrac{x^4}{4y^2}}\)} (y < 0)

d. \(\dfrac{y}{x}\) \(\times\) \(\sqrt{\dfrac{x^2}{y^4}}\) (x > 0 ; y \(\ne\)0)

e. \(\sqrt{\dfrac{9a^2}{16}}\)

f. \(\sqrt{10.16a^2}\) (a < 0)

g. \(\sqrt{a^4}\left(3-a\right)^2\) (a \(\ge\) 3)

h. \(\sqrt{\dfrac{2a^2b^4}{98}}\)

Answer 1

\(a.\sqrt{2a}.\sqrt{18a}=\sqrt{2a}.3\sqrt{2a}=3.2a=6a\)

\(b.\sqrt{3a.27ab^2}=\sqrt{9a^2b^2.9}=9\text{ |}ab\text{ |}\)

\(c.2y^2.\sqrt{\dfrac{x^4}{4y^2}}=2y^2.\dfrac{x^2}{-2y}=-x^2y\)

\(d.\dfrac{y}{x}.\sqrt{\dfrac{x^2}{y^4}}=\dfrac{y}{x}.\dfrac{x}{y^2}=\dfrac{1}{y}\)

\(e.\sqrt{\dfrac{9a^2}{16}}=\dfrac{3\text{ |}a\text{ |}}{4}\)

\(f.\sqrt{10.16a^2}=-4a\sqrt{10}\)

\(g.\sqrt{a^4\left(3-a\right)^2}=a^2\left(a-3\right)\)

\(h.\sqrt{\dfrac{2a^2b^4}{98}}\sqrt{\dfrac{a^2b^4}{49}}=\dfrac{b^2\text{ |}a\text{ |}}{7}\)