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Properties of arithmetic square root

For a≥0, b≥0a\ge0,\ b\ge0: ab=a⋅b,ab=ab (b>0)\sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\quad \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\ (b>0). These identities help factor quantities out of and into a radical.
The root of a product equals the product of the roots (for nonnegative factors)
The root of a quotient equals the quotient of the roots (denominator > 0)
Always check the domain: the radicand must be ≥0\ge0
Using the properties.
Product under the radical: √(ab)
4⋅5\sqrt{4\cdot5}
=25=2\sqrt{5}
4⋅5=4⋅5\sqrt{4\cdot5}=\sqrt{4}\cdot\sqrt{5}=25=2\sqrt{5}
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