Question

find the square root. the variable represents a nonnegative real number. \sqrt{a^{6}}

Explanation:

Step1: Recall square root property

The square root of \( x^n \) (for non - negative \( x \)) can be simplified using the property \( \sqrt{x^{m}}=x^{\frac{m}{2}} \) when \( m \) is even. Here, we have \( \sqrt{a^{6}} \), so we apply the formula \( \sqrt{x^{n}}=x^{\frac{n}{2}} \) with \( x = a \) and \( n = 6 \).

$$ \sqrt{a^{6}}=a^{\frac{6}{2}} $$

Step2: Simplify the exponent

Simplify the exponent \( \frac{6}{2} \).

$$ a^{\frac{6}{2}}=a^{3} $$

Answer:

\( a^{3} \)