How do you simplify $\sqrt{49 - x^{2}}$ $sqrt(49-x^2)$ ?

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Answer 1 · 2016-01-31T17:12:07

This expression cannot be simplified, but it can be re-expressed:

$\sqrt{49 - x^{2}} = \sqrt{7 - x} \sqrt{7 + x}$ $sqrt(49-x^2) = sqrt(7-x)sqrt(7+x)$

If $a \geq 0$ $a >= 0$ or $b \geq 0$ $b >= 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$

For any Real number $x$ $x$ , at least one of $7 - x \geq 0$ $7-x >= 0$ or $7 + x \geq 0$ $7+x >= 0$ , so we find:

$\sqrt{49 - x^{2}} = \sqrt{(7 - x) (7 + x)} = \sqrt{7 - x} \sqrt{7 + x}$ $sqrt(49-x^2) = sqrt((7-x)(7+x)) = sqrt(7-x)sqrt(7+x)$

How do you simplify sqrt(49-x^2)√49−x2sqrt(49-x^2)?