Question

Đưa thừa số ra ngoài dấu căn:

a.\(\sqrt{49.360}\)

b.\(-\sqrt{500.162}\)

c.\(\sqrt{125a^2}vớia< 0\)

d.\(\frac{1}{3}\sqrt{225a^2}\) với a tùy ý

Answer 1

a) \(\sqrt{49.360}=\sqrt{7^2.6^2.10}=7.6\sqrt{10}=42\sqrt{10}\)

b) \(-\sqrt{500.162}=-\sqrt{\left(2^2.5^2.5\right).\left(2.3^2.3^2\right)}\)

\(=-2.5.3.3\sqrt{5.2}=-90\sqrt{10}\)

c) \(\sqrt{125a^2}=\sqrt{5^2.a^2.5}=5\left|a\right|\sqrt{5}=-5a\sqrt{5}\) (do a <0)

d) \(\frac{1}{3}\sqrt{225a^2}=\frac{1}{3}\sqrt{15^2.a^2}=\frac{15}{3}\left|a\right|=5\left|a\right|\)

a < 0 thì suy ra \(\frac{1}{3}\sqrt{225a^2}=\frac{1}{3}\sqrt{15^2.a^2}=\frac{15}{3}\left|a\right|=5\left|a\right|=-5a\)

a>=0 thì suy ra \(\frac{1}{3}\sqrt{225a^2}=\frac{1}{3}\sqrt{15^2.a^2}=\frac{15}{3}\left|a\right|=5\left|a\right|=5a\)