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Properties of Square Roots

PRODUCT PROPERTY OF SQUARE ROOTS

For all positive real numbers $a$ and $b$ ,

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

That is, the square root of the product is the same as the product of the square roots.

QUOTIENT PROPERTY OF SQUARE ROOTS

For all positive real numbers $a$ and $b$ , $b\ne 0$ :

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

The square root of the quotient is the same as the quotient of the square roots.