Question

multiply. assume p is greater than or equal to zero, and write your answer in simplest form. $9sqrt{10} cdot 7sqrt{50p}$

Explanation:

Step1: Multiply the coefficients and the radicals separately

First, multiply the coefficients \(9\) and \(7\), and multiply the radicals \(\sqrt{10}\) and \(\sqrt{50p}\) using the property \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\).
So we have \(9\times7\times\sqrt{10\times50p}\)
\(9\times7 = 63\) and \(10\times50p=500p\), so now we have \(63\sqrt{500p}\)

Step2: Simplify the radical \(\sqrt{500p}\)

Factor \(500\) into perfect square and non - perfect square factors. \(500 = 100\times5\), and \(100\) is a perfect square (\(10^2\)).
Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 100\), \(b = 5p\)), we get \(\sqrt{500p}=\sqrt{100\times5p}=\sqrt{100}\times\sqrt{5p}=10\sqrt{5p}\)

Step3: Multiply the coefficient with the simplified radical part

Now we have \(63\times10\sqrt{5p}\)
\(63\times10 = 630\)

Answer:

\(630\sqrt{5p}\)