Question

radicals introduction to simplifying a radical expression with an even exponent simplify. \\(\sqrt{y^{36}}\\) assume that the variable represents a positive real number.

Explanation:

Step1: Recall the square root property

For a non - negative real number \(a\) and an even exponent \(n = 2k\), \(\sqrt{x^{2k}}=x^{k}\) (since \(x\) is a positive real number, we don't have to consider the absolute value).
Here, we have \(\sqrt{y^{36}}\), and we can rewrite the exponent \(36\) as \(2\times18\).

Step2: Apply the square root property

Using the property \(\sqrt{x^{2k}} = x^{k}\) with \(x = y\) and \(2k=36\) (so \(k = 18\)), we get \(\sqrt{y^{36}}=y^{18}\).

Answer:

\(y^{18}\)