1ruts gọn biểu thức : \(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^2}\)
rút gọn các biểu thức
a. \(\sqrt{13a}.\sqrt{\frac{52}{a}}\) với a > 0
b. \(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^2}\)
Rút gọn:
A = \(\sqrt{27.48\left(1-a^2\right)}\) với a > 1
B = \(\dfrac{1}{a-b}\sqrt{a^4\left(a-b\right)^2}\) với a > b
C = \(\sqrt{5a}.\sqrt{45a}-3a\) với a ≥ 0
D = \(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^2}\) với a tùy ý
a) Ta có: \(\sqrt{27\cdot48\left(1-a^2\right)}\)
\(=\sqrt{3^4\cdot4^2\cdot\left(1-a^2\right)}\)
\(=36\sqrt{1-a^2}\)
c) Ta có: \(\sqrt{5a}\cdot\sqrt{45a}-3a\)
\(=15a-3a=12a\)
b) Ta có: \(B=\dfrac{1}{a-b}\cdot\sqrt{a^4\cdot\left(a-b\right)^2}\)
\(=\dfrac{1}{a-b}\cdot a^2\cdot\left(a-b\right)\)
\(=a^2\)
d) Ta có: \(D=\left(3-a\right)^2-\sqrt{0.2}\cdot\sqrt{180a^2}\)
\(=a^2-6a+9-\sqrt{36a^2}\)
\(=a^2-6a+9-\left|6a\right|\)
\(=\left[{}\begin{matrix}a^2-6a+9-6a\left(a\ge0\right)\\a^2-6a+9+6a\left(a< 0\right)\end{matrix}\right.\)
\(=\left[{}\begin{matrix}a^2-12a+9\\a^2+9\end{matrix}\right.\)
\(A=9.4\left|1-a\right|=36\left(a-1\right)\) (a>1)
\(B=\dfrac{a^2\left|a-b\right|}{a-b}=\dfrac{a^2\left(a-b\right)}{a-b}=a^2\) (a>b)
\(C=5.3\left|a\right|-3a=15a-3a=12a\)
\(D=9-6a+a^2-6\left|a\right|=\left[{}\begin{matrix}a^2-12a+9\left(a\ge0\right)\\a^2+9\left(a< 0\right)\end{matrix}\right.\)
Rút gọn các biểu thức sau:
a. \(\sqrt{\dfrac{2a}{3}}.\sqrt{\dfrac{3a}{8}}\) với \(a\ge0;\)
b. \(\sqrt{13a}.\sqrt{\dfrac{52}{a}}\) với a > 0;
c. \(\sqrt{5a}.\sqrt{45a}-3a\) với \(a\ge0;\)
d. \(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^2}.\)
a) ĐS: ; b) ĐS: 26; c) ĐS: 12a
d) - = - 6a + 9 -
= - 6a + 9 - = - 6a + 9 - 6│a│.
Khi a ≥ 0 thì │a│= a.
Do đó - = - 6a + 9 -6a = - 12a + 9.
Khi a < 0 thì │a│= a.
Do đó - = - 6a + 9 + 6a = + 9.
Rút gọn
\(A=\sqrt{27.48\left(1-a^2\right)}vớia>1\)
\(B=\frac{1}{a-b}.\sqrt{a^4.\left(a-b\right)^2}\)Với a>b
\(C=\sqrt{5a}.\sqrt{45a}-3a\)với a> hoặc bằng 0
\(D=\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^2}\)Với a tùy ý
\(A=\sqrt{9.3.3.16\left(1-a^2\right)}=3.3.4.\left|1-a\right|=36\left(a-1\right)\)
\(B=\frac{1}{a-b}a^2.\left|a-b\right|=\frac{a^2\left(a-b\right)}{a-b}=a^2\)
\(C=\sqrt{5.45.a^2}-3a=\sqrt{5^2.3^2.a^2}-3a=15\left|a\right|-3a=15a-3a=12a\)
\(D=\left(3-a\right)^2-\sqrt{\frac{2.180}{10}a^2}=\left(3-a\right)^2-6\left|a\right|\)
Rút gọn biểu thức:
\(\sqrt{\frac{2a}{3}}.\sqrt{\frac{3a}{8}}vớia\ge0\)\(\sqrt{5a}.\sqrt{45a}-3avớia\ge0\)\(4\sqrt{16a^6}-6a^3\rightarrow kq2TH\)\(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^4}\)\(\sqrt{\frac{27.\left(a-3\right)^2}{48}}vớia< 3\)\(\frac{\sqrt{63y^3}}{\sqrt{7y}}vớiy>0\)\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^2}}vớia< 0,b\ne0\)\(\frac{a-b}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a^3}+\sqrt{b^3}}{a-b}\left(a\ge0;b\ge0;a\ne b\right)\)\(\frac{2a+\sqrt{ab}-3b}{2a-5\sqrt{ab}+3b}\left(a,b\ge0;4a\ne9b\right)\)1. Rút gọn biểu thức:
a) \(\sqrt{27\cdot48\cdot\left(1-a\right)^2}\)với a>1
b) \(\frac{1}{a-b}\cdot\sqrt{a^4\left(a-b\right)^2}\) với a>b
c) \(\sqrt{\frac{2a}{3}}\cdot\sqrt{\frac{3a}{8}}\)với \(a\ge0\)
d) \(\sqrt{13a}\cdot\sqrt{\frac{52}{a}}\)với a>0
e) \(\left(3-a\right)^2-\sqrt{0.2}\cdot\sqrt{180a^2}\)
Rút gọn biểu thức A=\(\sqrt{\left(-3\right)^2}\)-\(\sqrt{\left(3-\sqrt{2}\right)^2}\)
\(A=\sqrt{\left(-3\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\\ =\left|-3\right|-\left|3-\sqrt{2}\right|\\ =3-3+\sqrt{2}\\=\sqrt{2}\)
Rút gọn biểu thức:
\(A=\sqrt{\left(2-\sqrt{7}\right)^2}+\left(\sqrt{7}-1\right)^2\)
\(B=3\sqrt{\left(1,5\right)^2}-4\sqrt{\left(3-\sqrt{2}\right)^2}\)
\(A=\left|2-\sqrt{7}\right|+7-2\sqrt{7}+1\)
\(=\sqrt{7}-2+8-2\sqrt{7}\) \(=6-\sqrt{7}\)
\(B=3\cdot1,5-4\cdot\left|3-\sqrt{2}\right|\) \(=4,5-4\left(3-\sqrt{2}\right)\)
\(=4,5-12+4\sqrt{2}\) \(=4\sqrt{2}-7,5\)
Ta có: \(A=\sqrt{\left(2-\sqrt{7}\right)^2}+\left(\sqrt{7}-1\right)^2\)
\(=\sqrt{7}-2+8-2\sqrt{7}\)
\(=6-\sqrt{7}\)
a) \(\left(3-a\right)^2\sqrt{0,2}.\sqrt{180a^2}\)
b) \(\sqrt{50}-3\sqrt{98}+2\sqrt{8}+3\sqrt{32}-5\sqrt{18}\)
c) \(\left(\frac{1}{a-\sqrt{a}}+\frac{1}{a-2\sqrt{a+1}}\right)\div\frac{\sqrt{a-1}}{a-2\sqrt{a+}1}\)với \(a>0\)và \(a\ne1\)