Question

Simplify. (Assume all variables represent positive real numbers). Leave answer in radical form.

Answer 1

Answer:

$\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6} \sqrt{2b}$

Step-by-step explanation:

Given

$\sqrt{128a^{6}b^{13}}$

Required

Solve

$\sqrt{128a^{6}b^{13}}$

The expression can be split to:

$\sqrt{128a^{6}b^{13}} = \sqrt{128} * \sqrt{a^{6}} * \sqrt{b^{13}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64 * 2} * \sqrt{a^{6}} * \sqrt{b^{13}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{13}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{12 + 1}}$

$\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{12}} * \sqrt{b}$

So, we have:

$\sqrt{128a^{6}b^{13}} = 8 * \sqrt{2} * a^{6/2} * b^{12/2} * \sqrt{b}$

$\sqrt{128a^{6}b^{13}} = 8 * \sqrt{2} * a^{3} * b^{6} * \sqrt{b}$

Rewrite as:

$\sqrt{128a^{6}b^{13}} = 8 * a^{3} * b^{6}* \sqrt{2} * \sqrt{b}$

$\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6}* \sqrt{2b}$

$\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6} \sqrt{2b}$