What is q/p*sqrt(pq) ?

The solution to q/p*sqrt(pq) is (qsqrt(q))/(sqrt(p))

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simplify q/p*sqrt(pq)

simplify

\frac{q}{p} \cdot pq

\frac{q q}{p}

Solution steps

\frac{q}{p} pq

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{q pq}{p}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

pq = p q

= \frac{q p q}{p}

Apply radical rule:

a = a a

p = p p

= \frac{q p q}{p p}

Cancel the common factor:

p

= \frac{q q}{p}

\frac{4}{5} \cdot 10

100 \div 100

\frac{40}{25}

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3 45 x^{3} + 5 x