Question

question
simplify \\(\sqrt{25x^{12}}\\) completely given \\(x > 0\\).
answer attempt 1 out of 5

Explanation:

Step1: Apply square root property

We know that $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (for $a\geq0,b\geq0$). So, $\sqrt{25x^{12}}=\sqrt{25}\cdot\sqrt{x^{12}}$.

Step2: Simplify each square root

For $\sqrt{25}$, since $5^2 = 25$, we have $\sqrt{25}=5$. For $\sqrt{x^{12}}$, using the property $\sqrt{x^n}=x^{\frac{n}{2}}$ (when $x>0$), here $n = 12$, so $\sqrt{x^{12}}=x^{\frac{12}{2}}=x^6$.

Step3: Combine the results

Multiply the two simplified square roots: $5\cdot x^6 = 5x^6$.

Answer:

$5x^6$