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Ta có : 1,12(32) = 1,12 + 0,0032
Mà 0,0032 = 32/9990
Nên : 1,12(32) = 28/25 + 32/9990 = 556/495
Nhập vào máy : Sích mak
công thức (2n - 1) ( 2n + 1) x chạy từ 1 đến 15 ok
a) \(A=\dfrac{1}{\sqrt{25}}+\dfrac{\sqrt{49}}{\sqrt{36}}-\dfrac{2}{\sqrt{100}}.\)
\(=\dfrac{1}{5}+\dfrac{7}{6}-\dfrac{1}{5}.\)
\(=\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+\dfrac{7}{6}.\)
\(=0+\dfrac{7}{6}=\dfrac{7}{6}.\)
Vậy \(A=\dfrac{7}{6}.\)
b) \(B=\sqrt{\dfrac{0,01}{1,21}}+3.\dfrac{2}{\sqrt{10^2}+2^2+40}-\dfrac{3}{4}.\)
\(=\dfrac{1}{11}+3.\dfrac{2}{10+4+40}-\dfrac{3}{4}.\)
\(=\dfrac{1}{11}+3.\dfrac{1}{37}-\dfrac{3}{4}.\)
\(=\dfrac{1}{11}+\dfrac{1}{9}-\dfrac{3}{4}.\)
\(=\dfrac{36}{396}+\dfrac{44}{396}-\dfrac{297}{296}.\)
\(=-\dfrac{217}{396}.\)
Vậy \(B=-\dfrac{217}{396}.\)
a)\(\sqrt{0,01}-\sqrt{0,25}\)
=\(\sqrt{\left(0,1\right)^2}-\sqrt{\left(0,5\right)^2}\)
= 0,1 - 0,5 = - 0,4
b)\(0,5.\sqrt{100}-\sqrt{\dfrac{1}{4}}\)
=0,5.\(\sqrt{10^2}-\sqrt{\left(\dfrac{1}{2}\right)^2}\)
=0,5.10−\(\dfrac{1}{2}\)
= 5 - 0,5
= 4,5.
a) 0,1 - 0,5 = -0,4
b)0,5 . 10 - 0,5 = 5 - 0,5 = 4,5
thầy thông cảm máy em không có dấu căn.
\(\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\left(\dfrac{2}{7}\right)^2-\dfrac{4}{343}}=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4-\dfrac{4}{7}+\dfrac{4}{49}-\dfrac{4}{343}}\\ =\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4\cdot\left(1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}\right)}=\dfrac{1}{4}\)
a, \(15\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)-25\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)\)
\(=15\dfrac{1}{4}.\left(-\dfrac{7}{5}\right)-25\dfrac{1}{4}.\left(-\dfrac{7}{5}\right)\)
\(=-\dfrac{7}{5}.\left(15\dfrac{1}{4}-25\dfrac{1}{4}\right)\)
\(=-\dfrac{7}{5}.\left(-10\right)\)
\(=\dfrac{7}{5}.10\)
\(=\dfrac{7}{1}.2\)
\(=14\)
b, \(\sqrt{0.16}-\sqrt{0.25}\)
\(=0.4-0.5\)
\(=-0.1\)
\(\sqrt{484}-\dfrac{1}{\sqrt{5}}< \sqrt{529}-\dfrac{1}{19}< \sqrt{576}-\dfrac{1}{\sqrt{7}}< \sqrt{625}-\dfrac{1}{\sqrt{8}}\)
a: Để D là số nguyên thì \(3\sqrt{x}+5⋮2\sqrt{x}-1\)
\(\Leftrightarrow6\sqrt{x}+10⋮2\sqrt{x}-1\)
\(\Leftrightarrow2\sqrt{x}-1\in\left\{1;-1;13;-13\right\}\)
hay \(x\in\left\{1;0;49\right\}\)
b: Để E là số nguyên thì \(\sqrt{x}+2\inƯ\left(10\right)\)
\(\Leftrightarrow\sqrt{x}+2\in\left\{2;5;10\right\}\)
hay \(x\in\left\{0;9;64\right\}\)
c: Để F là số nguyên thì \(\sqrt{x}-3⋮\sqrt{x}+1\)
\(\Leftrightarrow\sqrt{x}+1-4⋮\sqrt{x}+1\)
\(\Leftrightarrow\sqrt{x}+1\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(x\in\left\{0;1;9\right\}\)
d: Để G là số nguyên thì \(3\sqrt{x}-6+5⋮\sqrt{x}-2\)
\(\Leftrightarrow\sqrt{x}-2\in\left\{1;-1;5;-5\right\}\)
hay \(x\in\left\{9;1;49\right\}\)
a) A = \(\left(-\dfrac{1}{5}\right)^3.5^3+0,75=-\dfrac{1}{125}.125+\dfrac{3}{4}=-1+\dfrac{3}{4}=-\dfrac{1}{4}\)
b) B = \(\sqrt{49}-2.\sqrt{25}=7-2.5=-3\)
\(S=\dfrac{1}{2}.\left(\dfrac{2}{\sqrt{1.3}}+\dfrac{2}{\sqrt{3.5}}+.......+\dfrac{2}{\sqrt{29.31}}\right)\)
\(S=\dfrac{1}{2}\left(1-\dfrac{1}{\sqrt{3}}+\dfrac{1}{\sqrt{3}}-\dfrac{1}{\sqrt{5}}+\dfrac{1}{\sqrt{5}}+.....-\dfrac{1}{\sqrt{29}}+\dfrac{1}{\sqrt{29}}-\dfrac{1}{\sqrt{31}}\right)\)
\(S=\dfrac{1}{2}.\left(1-\dfrac{1}{\sqrt{31}}\right)=\dfrac{1}{2}.\left(\dfrac{31-\sqrt{31}}{31}\right)=\dfrac{31-\sqrt{31}}{62}\)