How do you simplify $sqrt(49)/sqrt(500)$ ?

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Answer 1 · 2016-01-29T22:18:42

$sqrt(49)/sqrt(500)=7/(10sqrt(5))=(7sqrt(5))/50$

We will use the following properties:

$sqrt(49)/sqrt(500) = sqrt(7^2)/sqrt(10^2*5)$

$=7/(sqrt(10^2)sqrt(5))$

$=7/(10sqrt(5))$

We could finish here, or rationalize the denominator by multiplying the numerator and denominator by $sqrt(5)$ to obtain

$7/(10sqrt(5)) = (7sqrt(5))/(10sqrt(5)sqrt(5))$

$=(7sqrt(5))/(10*5)$

$=(7sqrt(5))/50$

How do you simplify sqrt(49)/sqrt(500)sqrt(49)/sqrt(500)?