Question

Rút gọn các biểu thức

a, \(\sqrt{27.48\left(1-a\right)^2}\) với a > 1

b, \(\frac{1}{a-b}.\sqrt{a^4\left(a-b\right)^2}\) với a > b

c, \(\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\)

Answer 1

a/ \(=\sqrt{36^2\left(1-a\right)^2}=36.\left|1-a\right|=36\left(a-1\right)=36a-36\)

b/ \(=\frac{1}{a-b}.a^2\left|a-b\right|=\frac{1}{a-b}.a^2\left(a-b\right)=a^2\)

c/ \(=\frac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}+\frac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{7}+1\right)^2}+\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}=\frac{\sqrt{7}+1+\sqrt{7}-1}{\sqrt{2}}=\frac{2\sqrt{7}}{\sqrt{2}}=\sqrt{14}\)