Question

10 points!!! What is sqr root 12x^8/ sqr root 3x^2 in simplest form

Answer 1

2x^3

Explanation:

`(√(12x^8))/(√(3x^2))`

Both top and bottom have square root . We can take square root in common

`\sqrt{(12x^8)/(3x^2) }`

simplify the exponent using exponential property

a^m / a^n = a^{m-n}, subtract the exponents

`\sqrt{(12x^8)/(3x^2) }`

`√(4x^6)`

`√(4) =2`

`√(x^6) =√(x^2 \cdot x^2 \cdot x^2) =x^3`

`√(4x^6)=2x^3`

Answer 2

2 x^3

Explanation:

sqrt(12 x^8)/ sqrt(3x^2)

combine into 1 term

sqrt(12x^8/3x^2)

when dividing exponents with the same base, we subtract

sqrt(12/3 x^(8-2))

sqrt(4 x^6)

sqrt(4) sqrt(x^6)

2 x^3