What is sqrt((147m^5n^7)/(441z^6)) ?

The solution to sqrt((147m^5n^7)/(441z^6)) is (m^2n^3sqrt(m)sqrt(n))/(sqrt(3)z^3)

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simplify sqrt((147m^5n^7)/(441z^6))

simplify

\frac{147 m ^{5} n ^{7}}{441 z ^{6}}

\frac{m ^{2} n ^{3} m n}{3 z ^{3}}

Solution steps

\frac{147 m ^{5} n ^{7}}{441 z ^{6}}

Cancel

\frac{147 m ^{5} n ^{7}}{441 z ^{6}} : \frac{m ^{5} n ^{7}}{3 z ^{6}}

= \frac{m ^{5} n ^{7}}{3 z ^{6}}

Apply radical rule:

\frac{a}{b} = \frac{a}{b},

assuming

a \geq 0, b \geq 0

= \frac{m ^{5} n ^{7}}{3 z ^{6}}

Simplify

m^{5} n^{7} : m^{2} n^{3} m n

= \frac{m ^{2} n ^{3} m n}{3 z ^{6}}

Simplify

3 z^{6} : 3 z^{3}

= \frac{m ^{2} n ^{3} m n}{3 z ^{3}}

(3.3) (4.5)

i^{107}

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\frac{x + 1}{x + 1} - \frac{4 x}{x - 1} + \frac{4}{x ^{2} - 1}

What is sqrt((147m^5n^7)/(441z^6)) ?
The solution to sqrt((147m^5n^7)/(441z^6)) is (m^2n^3sqrt(m)sqrt(n))/(sqrt(3)z^3)