Question

1. simplify \\(\sqrt{250}\\). express the answer in simplest form. \\(2\sqrt{5}\\) \\(5\sqrt{2}\\) \\(10\sqrt{5}\\) \\(5\sqrt{10}\\)

Explanation:

Step1: Factor 250

We need to factor 250 into a product of a perfect square and another number. We know that \(250 = 25\times10\), where 25 is a perfect square (\(25 = 5^2\)). So we can write \(\sqrt{250}=\sqrt{25\times10}\).

Step2: Use the square root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we have \(\sqrt{25\times10}=\sqrt{25}\times\sqrt{10}\).

Step3: Simplify \(\sqrt{25}\)

Since \(\sqrt{25} = 5\), we substitute this back to get \(5\times\sqrt{10}=5\sqrt{10}\).

Answer:

D. \(5\sqrt{10}\)