Question

How do I solve this?”USING SIMPLIFYING RADICALS WITH VARIABLES”

Answer 1

Answer:

$\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}$

Step-by-step explanation:

Given

$\sqrt{72a^8b^5$

Required

Simplify

Express 72 as 36 * 2

$\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8b^5}$

Express $b^5$ as $b^4*b$

$\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8*b^4*b}$

Reorder

$\sqrt{72a^8b^5} = \sqrt{36 *a^8*b^4* 2*b}$

Split:

$\sqrt{72a^8b^5} = \sqrt{36} *\sqrt{a^8} *\sqrt{b^4} * \sqrt{2*b}$

Simplify each term

$\sqrt{72a^8b^5} = 6 * a^{\frac{8}{2}} * b^{\frac{4}{2}} * \sqrt{2*b}$

$\sqrt{72a^8b^5} = 6 * a^4 * b^2 * \sqrt{2*b}$

$\sqrt{72a^8b^5} = 6a^4b^2 * \sqrt{2*b}$

$\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}$