Understanding Surds

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$Surds\ \ are\ \ numerical\ \ expressions\\ that\ \ involve\ \ irrational\ \ roots. \ They\ \ are\ \ \\irrational\ \ numbers.$

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Rule 1 : $\sqrt{xy}= \sqrt{x}*\sqrt{y}$.

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Rule 2: $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$.

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Rule 3: $(\sqrt x)^2 = x$.

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Note: $For\ \sqrt x\ \ to\ \ exist,\ x\ cannot\ be\ negative$.

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Examples

Problem 1

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Problem 2

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Problem 3

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Problem 4