Question

Đưa thừa số ra ngoài dấu căn :

a. \(\sqrt{9\text{6}}.\sqrt{\text{1}2\text{5}}\)

b.\(\sqrt{a^4.\text{6}^{\text{5}}}\)

c.\(\sqrt{a^{\text{6}}.b^{\text{1}\text{1}}}\)

d.\(\:\sqrt{a^{\text{3}}\left(\text{1}-a\right)^4}\)

Answer 1

a) Ta có: \(\sqrt{96}\cdot\sqrt{125}\)

\(=\sqrt{16}\cdot\sqrt{6}\cdot\sqrt{25}\cdot\sqrt{5}\)

\(=20\cdot\sqrt{30}\)

b) Ta có: \(\sqrt{a^4\cdot6^5}\)

\(=a^2\cdot36\cdot\sqrt{6}\)

c) Ta có: \(\sqrt{a^6\cdot b^{11}}\)

\(=\sqrt{a^6}\cdot\sqrt{b^{11}}\)

\(=\left|a^3\right|\cdot\left|b^5\right|\cdot\sqrt{b}\)

\(=a^3b^5\cdot\sqrt{b}\)

d) Ta có: \(\sqrt{a^3\left(1-a\right)^4}\)

\(=\sqrt{a^3}\cdot\sqrt{\left(1-a\right)^4}\)

\(=a\sqrt{a}\cdot\left(1-a\right)^2\)