Question

1. simplify the expression below.

\frac{\sqrt{294k^{30}}}{\sqrt{3k^{5}}}
a. $7k^{2}\sqrt{2}$
b. $7k^{3}\sqrt{2}$
c. $7k^{5}\sqrt{2}$
d. $7k^{12}\sqrt{2k}$

Explanation:

Step1: Combine radicals into one

$\sqrt{\frac{294k^{30}}{3k^5}}$

Step2: Simplify fraction inside radical

$\sqrt{98k^{25}}$

Step3: Factor into perfect squares

$\sqrt{49 \times 2 \times k^{24} \times k}$

Step4: Extract perfect square roots

$7k^{12}\sqrt{2k}$

Answer:

D. $7k^{12}\sqrt{2k}$