Question

Rút gọn:

a,\(\sqrt{4\left(a-3\right)^2}\)với a \(\ge\)3

b,\(\sqrt{9\left(b-2\right)^2}\)với b < 2

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

d,\(\sqrt{5a}.\sqrt{45a}-3a\)với a \(\ge\)0

e,\(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}\)với x > 0

Answer 1

a) \(\sqrt{4\left(a-3\right)^2}=\sqrt{2^2\left(a-3\right)^2}=2\sqrt{\left(a-3\right)^2}=2.\left|a-3\right|=2\left(a-3\right)=2a-6\) (Vì \(a\ge3\) )

Answer 2

b) \(\sqrt{9\left(b-2\right)^2}=\sqrt{3^2\left(b-2\right)^2}=3\sqrt{\left(b-2\right)^2}=3\left|b-2\right|=3\left(2-b\right)\)

                                                         \(=6-3b\) (vì b < 2 )

b) \(\sqrt{27.48\left(1-a\right)^2}=\sqrt{27.3.16.\left(1-a\right)^2}=\sqrt{81.16.\left(1-a\right)^2}\) 

                                         \(=\sqrt{9^2.4^2.\left(1-a\right)^2}=9.4\sqrt{\left(1-a\right)^2}=36.\left|1-a\right|=36\left(1-a\right)=36-36a\) (vì a > 1)

Answer 3

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

b)  \(\sqrt{9\left(b-2\right)^2}=3.\left|b-2\right|=3\left(2-b\right)\)

c)  \(\sqrt{27.48\left(1-a\right)^2}=36.\left|1-a\right|=36\left(a-1\right)\)

d)  \(\sqrt{5a}.\sqrt{45a}-3a=\sqrt{5a.45a}-3a=15a-3a=12a\)

e)  \(\frac{\sqrt{48x^3}}{\sqrt{3x^5}}=\sqrt{\frac{48x^3}{3x^5}}=\sqrt{\frac{16}{x^2}}=\frac{4}{x}\)