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What is the square root of 14 divided by the square root of 45?

1 Answer

Oct 18, 2015

(Nothing really pretty)
$\frac{\sqrt{14}}{\sqrt{45}} = \frac{\sqrt{21}}{9}$ $sqrt(14)/sqrt(45) = sqrt(21)/9$

Explanation:

$\frac{\sqrt{14}}{\sqrt{45}}$ $sqrt(14)/sqrt(45)$

Factoring:
$color(white)("XXXX")=(cancel(sqrt(2))*sqrt(7))/(sqrt(3)*sqrt(3)*sqrt(3)*cancel(sqrt(2)))$

Simplifying:
$color(white)("XXXX")=sqrt(7)/(3sqrt(3))$

Rationalizing the denominator (by multiplying both numerator and denominator by $(sqrt(3))$
$color(white)("XXXX")=sqrt(21)/9$

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