Question

multiply. assume t and u are greater than or equal to zero, and write your answer in simplest form.
$9\sqrt{15t} \cdot \sqrt{55u^2}$

Explanation:

Step1: Use product rule of square roots

The product rule of square roots states that \(\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}\) (for \(a\geq0,b\geq0\)). Also, we can multiply the coefficients (the number outside the square root) with each other and the square roots with each other. So, \(9\sqrt{15t}\cdot\sqrt{55u^{2}} = 9\sqrt{15t\times55u^{2}}\)

Step2: Simplify the product inside the square root

First, calculate \(15\times55 = 825\). So now we have \(9\sqrt{825u^{2}t}\)

Step3: Simplify the square root of \(u^{2}\) and factor 825

Since \(u\geq0\), \(\sqrt{u^{2}} = u\). Now factor 825: \(825=25\times33\), and \(\sqrt{25\times33}=\sqrt{25}\times\sqrt{33}=5\sqrt{33}\)

Step4: Multiply the coefficients and the simplified square root parts

We have \(9\times u\times5\sqrt{33t}\) (because \(\sqrt{825u^{2}t}=\sqrt{25\times33\times u^{2}\times t}=5u\sqrt{33t}\)). Then \(9\times5 = 45\), so the expression becomes \(45u\sqrt{33t}\)

Answer:

\(45u\sqrt{33t}\)