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a) √54 = √9.6 = 3√6
b) √108 = √36.3 = 6√3
c) 0,1√20000 = 0,1√10000.2= 0,1.100√2 = 10√2
d) -0,05.√28800 = -0,05.√14400.2 = -0,05.120√2 = -6√2
e)√7.63.a2 = √7.7.9.a2 = 7.3|a| = 21|a|
a/ \(0,1\sqrt{2.10000=0,1\sqrt{ }2.100^{ }2=0,1\cdot100\sqrt{ }2=10\sqrt{ }2}\)
b/ \(-0,05\sqrt{28800}=-0,05\sqrt{288\cdot100=-0,05\cdot10\sqrt{ }288=6\sqrt{ }2}\)
c/\(\sqrt{7\cdot63}a^2=\sqrt{7\cdot9\cdot7}a^2=21a^2\)
\(\sqrt{72a^{ }2b\sqrt{ }4=\sqrt{ }6\cdot9\left|\right|ab^{ }2=-3\sqrt{ }6ab^{ }2}\)
a. \(\sqrt{13^2-12^2}\)
=\(\sqrt{\left(13+12\right).\left(13-12\right)}\)
=\(\sqrt{25.1}\)
=\(\sqrt{25}.\sqrt{1}\)
=5.1
=5
b. \(\sqrt{17^2-8^2}\)
=\(\sqrt{\left(17+8\right).\left(17-8\right)}\)
=\(\sqrt{25.9}\)
=\(\sqrt{25}.\sqrt{9}\)
=5.3
=15
c. \(\sqrt{117^2-108^2}\)
=\(\sqrt{\left(117+108\right).\left(117-108\right)}\)
=\(\sqrt{225.9}\)
=\(\sqrt{225}.\sqrt{9}\)
=15.3
=45
d. \(\sqrt{313^2-312^2}\)
=\(\sqrt{\left(313+312\right).\left(313-312\right)}\)
=\(\sqrt{625.1}\)
=\(\sqrt{625}.\sqrt{1}\)
=25.1
=25
c.\(\sqrt{117^2-108^2}\)
a) \(\sqrt{27x^2}=\sqrt{3.\left(3x\right)^2}=\left|3x\right|.\sqrt{3}=3x\sqrt{3}\left(x>0\right)\)
b) \(\sqrt{8xy^2}=\left|y\right|.2\sqrt{2x}=-2y\sqrt{2x}\left(x\ge0,y\le0\right)\)
1) \(x\sqrt{13}=\sqrt{13x^2}\left(x\ge0\right)\)
2) \(x\sqrt{-15x}=-\left|x\right|\sqrt{15x}=-\sqrt{15x^3}\left(x< 0\right)\)
3) \(x\sqrt{2}=-\left|x\right|\sqrt{2}=-\sqrt{2x^2}\left(x\le0\right)\)
a) \(\sqrt{25\cdot96}=\sqrt{5^2\cdot2^5\cdot3}=\sqrt{5^2\cdot\left(2^2\right)^2\cdot2\cdot3}\)
\(=20\sqrt{6}\)
b) \(\sqrt{21\cdot75\cdot14}=\sqrt{2\cdot3^2\cdot5^2\cdot7^2}=105\sqrt{2}\)
c) \(y^2\sqrt{x^6\cdot y^8}=\sqrt{x^6\cdot y^4\cdot y^8}=\sqrt{\left(x^3\right)^2\cdot\left(y^6\right)^2}=x^3\cdot y^6\)
hì,giúp bn đc phần a thôi nha!!!
\(a,\sqrt{25.96}=\sqrt{25.16.6}=\sqrt{25}.\sqrt{16}.\sqrt{6}=5.4.\sqrt{6}=20\sqrt{6}\)
=.= hok tốt!!!
d) \(\dfrac{1}{3}\sqrt{225a^2}=\dfrac{1}{3}\sqrt{\left(15a\right)^2}=\dfrac{1}{3}\left|15a\right|=\left|5a\right|\)
\(\Rightarrow\left[{}\begin{matrix}a>0\Rightarrow d=5a\\a< 0\Rightarrow d=-5a\end{matrix}\right.\)
Giải:
a) \(\sqrt{49.360}\)
\(=\sqrt{7^2.3^2.2^2.10}\)
\(=7.3.2\sqrt{10}\)
\(=42\sqrt{10}\)
Vậy ...
b) \(-\sqrt{500.162}\)
\(=-\sqrt{10^2.5.9^2.2}\)
\(=-10.9\sqrt{10}\)
\(=-90\sqrt{10}\)
Vậy ...
c) \(\sqrt{125a^2}\)
\(=\sqrt{5^2.5.a^2}\)
\(=\sqrt{5^2.5.\left(-a\right)^2}\)
\(=-5a\sqrt{5}\)
Vậy ...
d) \(\dfrac{1}{3}\sqrt{225.a^2}\)
\(=\dfrac{1}{3}\sqrt{15^2.a^2}\)
\(=\dfrac{1}{3}.15.a^2\)
\(=5a^2\)
Vậy ...
Bài 1:
\(\sqrt{27a^2}=3a\sqrt{3}\)
Bài 2:
\(\dfrac{2}{3}\sqrt{3xy}=\sqrt{3xy\cdot\dfrac{4}{9}}=\sqrt{\dfrac{4}{3}xy}\)
Bài 3:
\(=4\sqrt{b}+2\cdot2\sqrt{10b}-3\cdot3\sqrt{10b}=4\sqrt{b}-5\sqrt{10b}\)
a/ \(\sqrt{a^4b^5}=a^2b^2\sqrt{b}\)
b/ \(\sqrt{a^6b^{11}}=a^3b^5\sqrt{b}\)
a )\(x\sqrt{7}\)
b )\(-2y\sqrt{2}\)
c )\(5x\sqrt{x}\)
d)\(4y^2\sqrt{3}\)
a: \(=\sqrt{9\cdot6}=3\sqrt{6}\)
b: \(=\sqrt{36\cdot3}=6\sqrt{3}\)
c: \(=\dfrac{1}{10}\cdot\sqrt{10000\cdot2}=\dfrac{1}{10}\cdot100\cdot\sqrt{2}=10\sqrt{2}\)
d: \(=-\dfrac{1}{20}\cdot\sqrt{14400\cdot2}=-\dfrac{1}{20}\cdot120\cdot\sqrt{2}=-6\sqrt{2}\)
e: \(=\sqrt{7\cdot7\cdot9\cdot a^2}=21\left|a\right|\)