Question

simplify the radical. assume
your answer
\\(\sqrt{q^{3}} = \square\\)

Explanation:

Step1: Rewrite the exponent

We can rewrite \( q^3 \) as \( q^{2 + 1}=q^2\times q \). So, \( \sqrt{q^3}=\sqrt{q^2\times q} \).

Step2: Use the property of square roots

The property of square roots states that \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0,b\geq0 \)). Applying this, we get \( \sqrt{q^2\times q}=\sqrt{q^2}\times\sqrt{q} \).

Step3: Simplify \( \sqrt{q^2} \)

Since \( \sqrt{q^2} = |q| \), but assuming \( q\geq0 \) (as is common when simplifying radicals without a negative sign indicated for the variable inside), \( \sqrt{q^2}=q \). So, \( \sqrt{q^2}\times\sqrt{q}=q\sqrt{q} \).

Answer:

\( q\sqrt{q} \)