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1.
\(\Leftrightarrow x-3=\dfrac{1}{8}\)
\(\Leftrightarrow x=\dfrac{25}{8}\)
a, \(=2\sqrt{7}-8+15\sqrt{7}-12=17\sqrt{7}-20\)
b, \(=2\sqrt{2}-10\sqrt{2}+4\sqrt{2}=-4\sqrt{2}\)
c, \(=\frac{3}{8}.\frac{4}{3}-2.\frac{2}{5}=\frac{1}{2}-\frac{4}{5}=-\frac{3}{10}\)
d, \(\sqrt{\left(\sqrt{3-1}\right)^2}-\sqrt{\left(\sqrt{3-2}\right)^2}=\sqrt{3-1}-\sqrt{3-2}=\sqrt{2}-\sqrt{1}=\sqrt{2}-1\)
e, \(\sqrt{2-3}\) không tồn tại
a) \(\sqrt{36}.\sqrt{121}+\sqrt[3]{-64}-\sqrt[3]{125}\)
\(=6.11+\left(-4\right)-5=66-9=57\)
b) \(\sqrt{75}+\sqrt{\left(\sqrt{3}-2\right)^2}-30\sqrt{\frac{3}{25}}\)
\(=\sqrt{25.3}+\left|\sqrt{3}-2\right|-30.\frac{\sqrt{3}}{\sqrt{25}}\)
\(=5\sqrt{3}+2-\sqrt{3}-30.\frac{\sqrt{3}}{5}\)
\(=5\sqrt{3}+2-\sqrt{3}-6\sqrt{3}=2-2\sqrt{3}\)
c) \(\sqrt{11-4\sqrt{7}}-\frac{12}{1+\sqrt{7}}=\sqrt{7-4\sqrt{7}+4}-\frac{12}{1+\sqrt{7}}\)
\(=\sqrt{\left(\sqrt{7}-2\right)^2}-\frac{12}{1+\sqrt{7}}=\left|\sqrt{7}-2\right|-\frac{12}{1+\sqrt{7}}\)
\(=\left(\sqrt{7}-2\right)-\frac{12}{\sqrt{7}+1}=\frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}+1\right)}{\sqrt{7}+1}-\frac{12}{\sqrt{7}+1}\)
\(=\frac{5-\sqrt{7}}{\sqrt{7}+1}-\frac{12}{\sqrt{7}+1}=\frac{-7-\sqrt{7}}{\sqrt{7}+1}\)
\(=\frac{-\sqrt{7}\left(\sqrt{7}+1\right)}{\sqrt{7}+1}=-\sqrt{7}\)
a: \(\Leftrightarrow2x+3=14-6\sqrt{5}\)
=>2x=11-6 căn 5
hay \(x=\dfrac{11-6\sqrt{5}}{2}\)
b: \(\Leftrightarrow\sqrt{7x}+5=11+4\sqrt{7}\)
=>căn 7x=6+4 căn 7
=>\(x=\dfrac{\left(6+4\sqrt{7}\right)^2}{7}\)
d: \(\Leftrightarrow\dfrac{1}{2}\sqrt{x-1}-\dfrac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17\)
=>-căn x-1=-17
=>căn x-1=17
=>x-1=289
=>x=290
Sửa đề: \(\sqrt[3]{64}+\sqrt[3]{-27}\)
Ta có: \(\sqrt[3]{64}+\sqrt[3]{-27}\)
\(=4+\left(-3\right)=1\)