Answer:
[tex]\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{72a^8b^5[/tex]
Required
Simplify
Express 72 as 36 * 2
[tex]\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8b^5}[/tex]
Express [tex]b^5[/tex] as [tex]b^4*b[/tex]
[tex]\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8*b^4*b}[/tex]
Reorder
[tex]\sqrt{72a^8b^5} = \sqrt{36 *a^8*b^4* 2*b}[/tex]
Split:
[tex]\sqrt{72a^8b^5} = \sqrt{36} *\sqrt{a^8} *\sqrt{b^4} * \sqrt{2*b}[/tex]
Simplify each term
[tex]\sqrt{72a^8b^5} = 6 * a^{\frac{8}{2}} * b^{\frac{4}{2}} * \sqrt{2*b}[/tex]
[tex]\sqrt{72a^8b^5} = 6 * a^4 * b^2 * \sqrt{2*b}[/tex]
[tex]\sqrt{72a^8b^5} = 6a^4b^2 * \sqrt{2*b}[/tex]
[tex]\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}[/tex]
