Question

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Answer 1

`d)D=1/2sqrt{a^10b^8}`

`=1/2sqrt{(a^5b^4)^2}`

`=1/2|a^5b^4|`

`=1/2b^4|a^5|`

`a>=0=>D=1/2b^4a^5`

`a<=0=>D=-1/2b^4a^5`

`e)sqrt{(2-sqrt3)^2}+sqrt2`

`=2-sqrt3+sqrt2``

`f)3sqrt5-sqrt{(1-sqrt5)^2}`

`=3sqrt5-(sqrt5-1)`

`=2sqrt5+1`

Answer 2

\(a.-\dfrac{1}{2}\sqrt{a^{10}.b^8}=-\dfrac{1}{2}a^5b^4\)

\(b.\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{2}\\=\sqrt{3}-\sqrt{2}+\sqrt{2}\\ =\sqrt{3}\)

\(c.3\sqrt{5}-\sqrt{\left(1-\sqrt{5}\right)^2}\\ =3\sqrt{5}-\sqrt{5}+1\\ =2\sqrt{5}+1\)