Đáp án:
Giải thích các bước giải:
`a)`
`2\sqrt{54}-(2)/(5).\sqrt{150}-2\sqrt{24}`
`=2.\sqrt{9.6}-(2)/(5).\sqrt{25.6}-2.\sqrt{4.6}`
`=2.3.\sqrt{6}-(2)/(5).5.\sqrt{6}-2.2.\sqrt{6}`
`=6\sqrt{6}-2\sqrt{6}-4\sqrt{6}`
`=(6-2-4).\sqrt{6}`
`=0.\sqrt{6}=0`
`b)`
`\sqrt{9+4\sqrt{5}}-\sqrt{(2-\sqrt{5})^2}`
`=\sqrt{4+2.2.\sqrt{5}+5}-|2-\sqrt{5}|`
`=\sqrt{(2+\sqrt{5})^2}-(\sqrt{5}-2)`
`=|2+\sqrt{5}|-\sqrt{5}+2`
`=2+\sqrt{5}-\sqrt{5}+2=4`
`c)`
`(2)/(\sqrt{5}+\sqrt{3})-\sqrt{(2)/(4-\sqrt{15})}+6\sqrt{1/3}`
`=(2.(\sqrt{5}-\sqrt{3}))/((\sqrt{5}+\sqrt{3}).(\sqrt{5}-\sqrt{3}))-\sqrt{(2.(4+\sqrt{15}))/((4-\sqrt{15}).(4+\sqrt{15}))}+\sqrt{36.(1)/(3)}`
`=(2.(\sqrt{5}-\sqrt{3}))/(5-3)-\sqrt{(8+2\sqrt{15})/(16-15)}+\sqrt{4.3}`
`=\sqrt{5}-\sqrt{3}-\sqrt{8+2\sqrt{15}}+2\sqrt{3}`
`=\sqrt{5}-\sqrt{3}-\sqrt{5+2\sqrt{3}.\sqrt{5}+3}+2\sqrt{3}`
`=\sqrt{5}-\sqrt{3}-\sqrt{(\sqrt{5}+\sqrt{3})^2}+2\sqrt{3}`
`=\sqrt{5}-\sqrt{3}-(\sqrt{5}+\sqrt{3})+2\sqrt{3}`
`=\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}+2\sqrt{3}`
`=(\sqrt{5}-\sqrt{5})-(\sqrt{3}+\sqrt{3}-2\sqrt{3})=0`
`d)`
`(1+(x+\sqrt{x})/(\sqrt{x}+1)).(1-(x-\sqrt{x})/(\sqrt{x}-1))(x>=0;x\ne1)`
`=(1+(\sqrt{x}.(\sqrt{x}+1))/(\sqrt{x}+1)).(1-(\sqrt{x}(\sqrt{x}-1))/(\sqrt{x}-1))`
`=(1+\sqrt{x}).(1-\sqrt{x})`
`=1-x`
