Answer:
[tex]\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6} \sqrt{2b}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{128a^{6}b^{13}}[/tex]
Required
Solve
[tex]\sqrt{128a^{6}b^{13}}[/tex]
The expression can be split to:
[tex]\sqrt{128a^{6}b^{13}} = \sqrt{128} * \sqrt{a^{6}} * \sqrt{b^{13}}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = \sqrt{64 * 2} * \sqrt{a^{6}} * \sqrt{b^{13}}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{13}}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{12 + 1}}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = \sqrt{64} * \sqrt{2} * \sqrt{a^{6}} * \sqrt{b^{12}} * \sqrt{b}[/tex]
So, we have:
[tex]\sqrt{128a^{6}b^{13}} = 8 * \sqrt{2} * a^{6/2} * b^{12/2} * \sqrt{b}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = 8 * \sqrt{2} * a^{3} * b^{6} * \sqrt{b}[/tex]
Rewrite as:
[tex]\sqrt{128a^{6}b^{13}} = 8 * a^{3} * b^{6}* \sqrt{2} * \sqrt{b}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6}* \sqrt{2b}[/tex]
[tex]\sqrt{128a^{6}b^{13}} = 8 a^{3} b^{6} \sqrt{2b}[/tex]
