Question

simplify. assume t is greater than or equal to zero.\\(sqrt{8t^{2}}\\)

Explanation:

Step1: Factor the radicand

We can factor \(8t^2\) as \(4\times2\times t^2\), so \(\sqrt{8t^2}=\sqrt{4\times2\times t^2}\).

Step2: Use the property of square roots

Recall that \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\)) and \(\sqrt{a^2}=a\) (for \(a\geq0\)). So we can split the square root:
\(\sqrt{4\times2\times t^2}=\sqrt{4}\cdot\sqrt{2}\cdot\sqrt{t^2}\)
Since \(t\geq0\), \(\sqrt{t^2}=t\) and \(\sqrt{4} = 2\). So substituting these values in, we get:
\(2\cdot\sqrt{2}\cdot t=2t\sqrt{2}\)

Answer:

\(2t\sqrt{2}\)