Question

Answer 1

`a)5\sqrt{1/5}+1/2\sqrt{20}+\sqrt{5}`

`=\sqrt{[5^2]/5}+2/2\sqrt{5}+\sqrt{5}`

`=\sqrt{5}+\sqrt{5}+\sqrt{5}=3\sqrt{5}`

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`b)0,1\sqrt{200}+2\sqrt{0,08}+0,4\sqrt{50}`

`=0,1.10\sqrt{2}+2. 1/5\sqrt{2}+0,4.5\sqrt{2}`

`=\sqrt{2}+2/5\sqrt{2}+2\sqrt{2}=17/5\sqrt{2}`

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`c)\sqrt{ab}+2\sqrt{b/a}-\sqrt{a/b}+\sqrt{1/[ab]}`

`=\sqrt{ab}+2\sqrt{[ab]/[a^2]}-\sqrt{[ab]/[b^2]}+\sqrt{[ab]/[(ab)^2]}`

`=\sqrt{ab}+2/[|a|]\sqrt{ab}-1/[|b|]\sqrt{ab}+1/[|ab|]\sqrt{ab}`

`=(1+2/[|a|]-1/[|b|]+1/[|ab|])\sqrt{ab}`