Question

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

Answer 1

`√(72a^8b^5) = 6a^4b^2 √(2b)`

Explanation:

Given

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

Required

Simplify

Express 72 as 36 * 2

`√(72a^8b^5) = √(36 * 2*a^8b^5)`

Express
`b^5` as
`b^4*b`

`√(72a^8b^5) = √(36 * 2*a^8*b^4*b)`

Reorder

`√(72a^8b^5) = √(36 *a^8*b^4* 2*b)`

Split:

`√(72a^8b^5) = √(36) *√(a^8) *√(b^4) * √(2*b)`

Simplify each term

`√(72a^8b^5) = 6 * a^{(8)/(2)} * b^{(4)/(2)} * √(2*b)`

`√(72a^8b^5) = 6 * a^4 * b^2 * √(2*b)`

`√(72a^8b^5) = 6a^4b^2 * √(2*b)`

`√(72a^8b^5) = 6a^4b^2 √(2b)`