Question

question 10
simplify: \\(\sqrt{\frac{128a^{13}b^7}{2a}}\\)
\\(4a^6b\sqrt{8ab}\\)
\\(7a^6b\sqrt{ab}\\)
\\(7a^6b\sqrt{ab}\\)
\\(4a^6b\sqrt{6ab}\\)

Explanation:

Step1: Simplify fraction inside root

$\sqrt{\frac{98a^{13}b^3}{2a}} = \sqrt{49a^{12}b^3}$

Step2: Split root into product terms

$\sqrt{49} \cdot \sqrt{a^{12}} \cdot \sqrt{b^3}$

Step3: Simplify each radical term

$\sqrt{49}=7$, $\sqrt{a^{12}}=a^6$, $\sqrt{b^3}=b\sqrt{ab}$

Step4: Combine simplified terms

$7 \cdot a^6 \cdot b\sqrt{ab} = 7a^6b\sqrt{ab}$

Answer:

$7a^6b\sqrt{ab}$