Questions: Simplify the radical expression. √(28 x^10)

Solution Steps

To simplify the radical expression \(\sqrt{28 x^{10}}\), we need to break it down into its prime factors and simplify the square root of each part separately. We can express \(28\) as \(4 \times 7\) and \(x^{10}\) as \((x^5)^2\). Then, we can take the square root of each part.

We start with the expression \(\sqrt{28 x^{10}}\). We can break down \(28\) into its prime factors: \(28 = 4 \times 7\). Also, we can express \(x^{10}\) as \((x^5)^2\).

Using the properties of square roots, we can simplify: \[ \sqrt{28 x^{10}} = \sqrt{4 \times 7 \times (x^5)^2} \] Since \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we get: \[ \sqrt{4 \times 7 \times (x^5)^2} = \sqrt{4} \times \sqrt{7} \times \sqrt{(x^5)^2} \]

We know that \(\sqrt{4} = 2\) and \(\sqrt{(x^5)^2} = x^5\). Therefore: \[ \sqrt{4} \times \sqrt{7} \times \sqrt{(x^5)^2} = 2 \times \sqrt{7} \times x^5 \]

Final Answer