Ae giúp mk vs ngu nhất phần căn bậc 3 còn mấy còn lại thì ok
\(\sqrt[3]{\frac{-1}{2}}.\sqrt[3]{-18}.\sqrt[3]{-3}\)
K
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28 tháng 7 2017
a)\(\frac{21}{\sqrt{14}}\)=\(\frac{21.\sqrt{14}}{14}\)=\(\frac{3\sqrt{14}}{2}\)
b)\(\frac{3}{\sqrt{2}}+\frac{\sqrt{2}}{3}=\frac{3\sqrt{2}}{2}+\frac{\sqrt{2}}{3}=\frac{9\sqrt{2}}{6}+\frac{2\sqrt{2}}{6}=\frac{11\sqrt{2}}{6}\)
c)=\(-46\sqrt{5}\)
PD
4
24 tháng 10 2018
\(\frac{5\left(\sqrt{6}-1\right)\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}+\frac{\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}{\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)}+\sqrt{\left(\sqrt{2}\right)^2-2\sqrt{2}+1}\)
\(=\frac{5\left(\sqrt{6}-1\right)^2}{5}-\frac{\left(\sqrt{2}-\sqrt{3}\right)^2}{1}+\sqrt{\left(\sqrt{2}-1\right)^2}\)
\(=\left(\sqrt{6}-1\right)^2-\left(\sqrt{2}-\sqrt{3}\right)^2+\left(\sqrt{2}-1\right)\)
\(=6-2\sqrt{6}+1-2+2\sqrt{6}-3+\sqrt{2}-1=\sqrt{2}\)
KT
7 tháng 7 2018
\(A=\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
\(\Rightarrow\)\(\frac{A}{\sqrt{2}}=\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}\)
\(=\frac{2+\sqrt{3}}{2+\left(\sqrt{3}+1\right)}+\frac{2-\sqrt{3}}{2-\left(\sqrt{3}-1\right)}\)
\(=\frac{2+\sqrt{3}}{3+\sqrt{3}}+\frac{2-\sqrt{3}}{3-\sqrt{3}}\)
\(=\frac{\left(2+\sqrt{3}\right)\left(\sqrt{3}-1\right)}{\sqrt{3}\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}+\frac{\left(2-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{\sqrt{3}\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=\frac{\sqrt{3}+1}{\sqrt{3}\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}+\frac{\sqrt{3}-1}{\sqrt{3}\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(=\frac{2\sqrt{3}}{2\sqrt{3}}=1\)
NT
3
22 tháng 6 2019
\(\sqrt{3-2\sqrt{2}}=\sqrt{\left(\sqrt{2}\right)^2-2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}-1\right)^2}=|\sqrt{2}-1|=\sqrt{2}-1\)
Tương tự \(\sqrt{4-2\sqrt{3}}=\sqrt{3}-1\); \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)
\(\Rightarrow BTT=\sqrt{2}-1+\sqrt{3}-1+2-\sqrt{3}=\sqrt{2}\)
TP
23 tháng 6 2019
\(\sqrt{3-2\sqrt{2}}+\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(=\sqrt{2-2\sqrt{2}+1}+\sqrt{3-2\sqrt{3}+1}-\sqrt{4-4\sqrt{3}+3}\)
\(=\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=\sqrt{2}-1+\sqrt{3}-1-2+\sqrt{3}\)
\(=2\sqrt{3}+\sqrt{2}-4\)
17 tháng 10 2020
a, để ý a có nghĩa thì 2x+1 \(\ge\)0 vì (\(x^2\) + 1\(\ge\)1, \(\forall\) x)\(\Rightarrow\)
\(\Rightarrow\) \(x\text{}\text{}\ge\)\(\frac{-1}{2}\)
HP
19 tháng 10 2020
a, \(\left\{{}\begin{matrix}2x-1\ne0\\\frac{x^2}{2x-1}\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{1}{2}\\2x-1>0\end{matrix}\right.\Leftrightarrow x>\frac{1}{2}\)
b, \(\frac{\sqrt[3]{625}}{\sqrt[3]{5}}-\sqrt[3]{-216}.\sqrt[3]{\frac{1}{27}}=\frac{\sqrt[3]{5^3.5}}{\sqrt[3]{5}}-\sqrt[3]{\left(-6\right)^3}.\sqrt[3]{\left(\frac{1}{3}\right)^3}\)
\(=\frac{5\sqrt[3]{5}}{\sqrt[3]{5}}+6.\frac{1}{3}=5+2=7\)
RA
1
7 tháng 10 2020
Ta có: \(\sqrt{18}-\frac{1}{3}\sqrt{72}-\sqrt{8}+\frac{2-3\sqrt{2}}{3-\sqrt{2}}\)
\(=3\sqrt{2}-\frac{6\sqrt{2}}{3}-2\sqrt{2}+\frac{\left(3+\sqrt{2}\right)\left(2-3\sqrt{2}\right)}{9-2}\)
\(=3\sqrt{2}-2\sqrt{2}-2\sqrt{2}-\sqrt{2}\)
\(=-2\sqrt{2}\)
\(\sqrt[3]{-\frac{1}{2}}\cdot\sqrt[3]{-18}\cdot\sqrt[3]{-3}\)
\(=\sqrt[3]{\left(-\frac{1}{2}\right)\cdot\left(-18\right)\cdot\left(-3\right)}\)
\(=\sqrt[3]{-27}=-3\)
\(\sqrt[3]{-\frac{1}{2}}.\sqrt[3]{-18}.\sqrt[3]{-3}=\sqrt[3]{\left(-\frac{1}{2}\right).\left(-18\right).\left(-3\right)}=\sqrt[3]{-27}=-3\)