Question

simplify. assume f is greater than or equal to zero. $sqrt{126f^{6}}$

Explanation:

Step1: Factor 126

$126 = 9\times14$, so $\sqrt{126f^{6}}=\sqrt{9\times14\times f^{6}}$

Step2: Apply square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{9\times14\times f^{6}}=\sqrt{9}\cdot\sqrt{14}\cdot\sqrt{f^{6}}$

Step3: Simplify square - roots

$\sqrt{9} = 3$, $\sqrt{f^{6}}=f^{3}$, so $\sqrt{9}\cdot\sqrt{14}\cdot\sqrt{f^{6}}=3f^{3}\sqrt{14}$

Answer:

$3f^{3}\sqrt{14}$