Question

Using the quotient property of radicals, what is the simplified form of √12x⁸/√3x², where x ≥ 0?

1) 4x³√3
2) 4x⁴√3
3) 4x⁵√3
4) 4x⁶√3

Answer 1

The simplified form of \(\sqrt{12x^8}/\sqrt{3x^2}\) is 2x³. Given options appear to have a typo as none match the correct simplification.

Step-by-step explanation:

To simplify the expression \(\sqrt{12x^8}/\sqrt{3x^2}\), where x ≥ 0, using the quotient property of radicals, we first combine the two radicals into one:

\(\sqrt{12x^8/3x^2}\) = \(\sqrt{4x^6}\)

Since 4 is a perfect square and x^6 is an even power, they can both be simplified:

\(\sqrt{4x^6}\) = 2x^3

Therefore, the simplified form of the original expression is 2x^3, which matches option 1) 4x³\(\sqrt{3}\), suggesting there could be a typo in the provided options.