How do I divide $sqrt(300x^18)/sqrt(2x)$ ?

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Answer 1 · 2017-03-06T20:54:09

$5 sqrt(6x^17) = 5sqrt(6)x^(17/2)$ assuming $x$ is positive,

otherwise $(5 sqrt(6)sqrt(x^18))/sqrt(x)$

Use the square root property: $(sqrt(m))/(sqrt(n)) = sqrt(m/n)$

$(sqrt(300 x^18))/(sqrt(2x)) = sqrt((300 x^18)/(2x)) = sqrt((150x^18)/x)$

Use the exponent rules: $x^m/x^n = x^(m-n)$ and $x^mx^n = x^(m+n)$

$sqrt((150x^18)/x)= sqrt(150x^17)$

Use the square root property: $sqrt(m*n) = sqrt(m) sqrt(n)$

$= sqrt(25 * 6 x^17) = sqrt(25)sqrt(6) sqrt(x^17)$

$= 5 sqrt(6x^17)$

Remember that $sqrt(m) = m^(1/2)$

So $5 sqrt(6x^17) = 5sqrt(6)x^(17/2)$

How do I divide sqrt(300x^18)/sqrt(2x)sqrt(300x^18)/sqrt(2x)?