For these real square-root laws, the radicands are non-negative; a denominator radicand must be stri

Question

For these real square-root laws, the radicands are non-negative; a denominator radicand must be strictly positive. Thus the product law uses $a,b\ge0$, and the quotient law uses $a\ge0,b>0$.

A surd is an expression that involves a root (such as a square root, cube root, etc.) and cannot be simplified into a rational number.

$\sqrt{ab}=\sqrt{a}\times \sqrt{b}$

$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

Accepted Answer

A surd is an irrational root expression that cannot be simplified to a rational number; $\sqrt{ab}=\sqrt a\sqrt b$ and $\sqrt{\frac ab}=\frac{\sqrt a}{\sqrt b}$ under the usual non-negative domain conditions.

Surds

Surds

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