Question

text to speech calculator highlighter incorrect 1 try left. try once more write the expression in radical notation. (5p)^(1/2) =

Explanation:

Step1: Recall exponent to radical rule

The rule for converting an exponent of the form \(a^{\frac{1}{n}}\) to radical notation is \(a^{\frac{1}{n}}=\sqrt[n]{a}\). When \(n = 2\), we can write it as \(\sqrt{a}\) (since the square root is the most common and the index 2 is often omitted for square roots). For the expression \((5p)^{\frac{1}{2}}\), using the rule \(a^{\frac{1}{n}}=\sqrt[n]{a}\) with \(a = 5p\) and \(n=2\), we get \(\sqrt{5p}\).

Step2: Construct the radical

We need to represent \((5p)^{\frac{1}{2}}\) using the radical symbols provided. The square root symbol \(\sqrt{\square}\) is appropriate here (since the exponent is \(\frac{1}{2}\), which corresponds to a square root). We put \(5p\) inside the square root. So \((5p)^{\frac{1}{2}}=\sqrt{5p}\).

Answer:

\(\sqrt{5p}\)