Question

Answer 1

`1)A=\sqrt{75}-5\sqrt{(1-\sqrt{3})^2}`

`A=\sqrt{5^2 .3}-5|1-\sqrt{3}|`

`A=5\sqrt{3}-5(\sqrt{3}-1)`

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

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`2)B=[\sqrt{10}-\sqrt{6}]/[\sqrt{5}-\sqrt{3}]-1/[\sqrt{2}+1]`

`B=[(\sqrt{10}-\sqrt{6})(\sqrt{5}+\sqrt{3})]/[5-3]-[\sqrt{2}-1]/[2-1]`

`B=[5\sqrt{2}+\sqrt{30}-\sqrt{30}-3\sqrt{2}]/2-[\sqrt{2}-1]/1`

`B=[2\sqrt{2}]/2-\sqrt{2}+1`

`B=\sqrt{2}-\sqrt{2}+1=1`

Answer 2

1: \(A=5\sqrt{3}-5\left(\sqrt{3}-1\right)\)

\(=5\sqrt{3}-5\sqrt{3}+5=5\)

2: \(B=\dfrac{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}{\sqrt{5}-\sqrt{3}}-\left(\sqrt{2}-1\right)\)

\(=\sqrt{2}-\sqrt{2}+1=1\)