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Tính:
a, √49 . √144+ √256 : √64
= 7 . 12 + 16 : 8
= 84 + 2
= 86
b, 72 : √2^2.36.3^2- √225
= 72: 2.6.3-15
= -13
Lời giải:
a)
\(\sqrt{144}.\sqrt{\frac{49}{69}}\sqrt{0,01}=12.\frac{7}{\sqrt{69}}.0,1=\frac{8,4}{\sqrt{69}}=\frac{42\sqrt{69}}{345}\)
b)
\(\sqrt{0,25}-\sqrt{225}+\sqrt{2,25}=\sqrt{0,5^2}-\sqrt{15^2}+\sqrt{1,5^2}\)
\(=0,5-15+1,5=-13\)
c)
\(72:\sqrt{3^3+3^2}-3\sqrt{5^2-3^2}\)
\(=\frac{72}{\sqrt{36}}-3\sqrt{16}=\frac{72}{6}-3.4=12-12=0\)
\(a)\) \(A=\sqrt{49}-2\sqrt{36}+3\sqrt{4}\)
\(A=7-2.6+3.2\)
\(A=7-12+6\)
\(A=1\)
\(b)\) \(B=\frac{1}{2}\sqrt{\frac{144}{225}}-7\sqrt{100}+4\sqrt{\frac{361}{400}}\)
\(B=\frac{1}{2}.\frac{4}{5}-7.10+4.\frac{19}{20}\)
\(B=\frac{2}{5}-70+\frac{19}{5}\)
\(B=\frac{-329}{5}\)
Chúc bạn học tốt ~
a: \(\sqrt{169}-\sqrt{225}\)
\(=\sqrt{13^2}-\sqrt{15^2}\)
=13-15
=-2
b: \(\dfrac{\sqrt{144}}{9}\)
\(=\dfrac{\sqrt{12^2}}{9}\)
\(=\dfrac{12}{9}=\dfrac{4}{3}\)
c: \(\sqrt{18}:\sqrt{2}=\sqrt{\dfrac{18}{2}}=\sqrt{9}=3\)
a,\(\sqrt{\left(2-\sqrt{5}\right)^2}-\sqrt{5}\)
\(=|^{ }_{ }2-\sqrt{5}|^{ }_{ }-\sqrt{5}\)
\(=\sqrt{5}-2-\sqrt{5}\)(vì \(2-\sqrt{5}< 0\))
=-2
b,\(\sqrt{16}\cdot\sqrt{25}+\sqrt{256}\cdot\sqrt{64}\)
\(=4\cdot5-16\cdot8=20+128=148\)
c,\(\sqrt{\left(\sqrt{2}-3\right)^2}-\sqrt{\left(5-\sqrt{2}\right)^2}\)
\(=|^{ }_{ }\sqrt{2}-3|^{ }_{ }-|^{ }_{ }5-\sqrt{2}|^{ }_{ }\)
\(=3-\sqrt{2}-5+\sqrt{2}\)(vì \(\sqrt{2}-3< 0;5-\sqrt{2}>0\))
\(=-2\)
a. ĐKXĐ: $x\geq 1$
PT $\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{3}{2}.\sqrt{9}.\sqrt{x-1}+24.\sqrt{\frac{1}{64}}.\sqrt{x-1}=-17$
$\Leftrightarrow \frac{1}{2}\sqrt{x-1}-\frac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17$
$\Leftrightarrow -\sqrt{x-1}=-17$
$\Leftrightarrow \sqrt{x-1}=17$
$\Leftrightarrow x-1=289$
$\Leftrightarrow x=290$
b. ĐKXĐ: $x\geq \frac{1}{2}$
PT $\Leftrightarrow \sqrt{9}.\sqrt{2x-1}-0,5\sqrt{2x-1}+\frac{1}{2}.\sqrt{25}.\sqrt{2x-1}+\sqrt{49}.\sqrt{2x-1}=24$
$\Leftrightarrow 3\sqrt{2x-1}-0,5\sqrt{2x-1}+2,5\sqrt{2x-1}+7\sqrt{2x-1}=24$
$\Leftrightarrow 12\sqrt{2x-1}=24$
$\Leftrihgtarrow \sqrt{2x-1}=2$
$\Leftrightarrow x=2,5$ (tm)
c. ĐKXĐ: $x\geq 2$
PT $\Leftrightarrow \sqrt{36}.\sqrt{x-2}-15\sqrt{\frac{1}{25}}\sqrt{x-2}=4(5+\sqrt{x-2})$
$\Leftrightarrow 6\sqrt{x-2}-3\sqrt{x-2}=20+4\sqrt{x-2}$
$\Leftrightarrow \sqrt{x-2}=-20< 0$ (vô lý)
Vậy pt vô nghiệm
\(3\sqrt{144}-5\sqrt{49}+\dfrac{1}{2}\sqrt{36}\)
\(=3.12-5.7+\dfrac{1}{2}.6\)
\(=36-35+3=4\)
a. bấm máy tính nó nói max nặng
b.\(\sqrt{16}.\sqrt{25}+\sqrt{256.\sqrt{64}}\)
=\(\sqrt{4^2}.\sqrt{5^2}+\sqrt{16^2.8}\)
=/4/./5/+/16/./2/\(\sqrt{2}\)
=4.5+16.2\(\sqrt{2}\)
=20+32\(\sqrt{2}\)
c.\(\sqrt{\left(2-\sqrt{3}\right)^2}-\sqrt{\left(5-\sqrt{2}\right)^2}\)
=/\(2-\sqrt{3}\)/-/5\(-\sqrt{2}\)/
=\(2-\sqrt{3}-5-\sqrt{2}\)
=\(\left(2-5\right)-\left(\sqrt{3}-\sqrt{2}\right)\)
=\(-3-\sqrt{3}-\sqrt{2}\)
= -6,146
\(a,\sqrt{49}.\sqrt{144}+\sqrt{256}:\sqrt{64}\\ =7.12+16:8\\ =84+2\\ =86\\ b,72:\sqrt{2^3.3^2.36}-\sqrt{225}\\ =72:\sqrt{1296}-25\\ =72:36-25\\ =2-25\\ =-23\)