Câu 2:
\(\frac{2\sqrt3-3\sqrt2}{\sqrt3-\sqrt2}+\frac{5}{\sqrt6+1}+\sqrt{\left(2\sqrt3+1\right)^2}\)
\(=\frac{-\sqrt6\left(\sqrt3-\sqrt2\right)}{\sqrt3-\sqrt2}+\frac{5\left(\sqrt6-1\right)}{\left(\sqrt6+1\right)\left(\sqrt6-1\right)}+2\sqrt3+1\)
\(=-\sqrt6+\sqrt6-1+2\sqrt3+1=2\sqrt3\)
=>Chọn A
Câu 4: \(\sqrt{9+4\sqrt5}+\sqrt{14-6\sqrt5}+\sqrt{\left(2\sqrt7-5\right)^2}\)
\(=\sqrt{\left(\sqrt5+2\right)^2}+\sqrt{\left(3-\sqrt5\right)^2}+2\sqrt7-5\)
\(=\sqrt5+2+3-\sqrt5+2\sqrt7-5=2\sqrt7\)
=>Chọn D
Câu 5:
\(\sqrt{\left(\sqrt3+2\right)^2}-\sqrt{11-6\sqrt2}-\sqrt{3-2\sqrt2}\)
\(=2+\sqrt3-\sqrt{\left(3-\sqrt2\right)^2}-\sqrt{\left(\sqrt2-1\right)^2}\)
\(=2+\sqrt3-3+\sqrt2-\sqrt2+1=\sqrt3\)
Câu 6:
\(\sqrt{16x-32}+\sqrt{25x-50}-\sqrt{9x-18}=96\)
=>\(4\cdot\sqrt{x-2}+5\cdot\sqrt{x-2}-3\cdot\sqrt{x-2}=96\)
=>\(6\cdot\sqrt{x-2}=96\)
=>\(\sqrt{x-2}=16\)
=>x-2=256
=>x=258
=>Chọn D
Câu 7:
\(\sqrt{3x+4}+\sqrt{27x+36}+\sqrt{12x+16}=30\)
=>\(\sqrt{3x+4}+3\cdot\sqrt{3x+4}+2\cdot\sqrt{3x+4}=30\)
=>\(6\cdot\sqrt{3x+4}=30\)
=>\(\sqrt{3x+4}=5\)
=>3x+4=25
=>3x=21
=>x=7
=>Chọn A
