solve 3√12 10√3-6/√3?

To solve this expression, we can simplify it step by step.

Step 1: Simplify the cube root of 12.

The cube root of 12 is not a perfect cube number. We can write it as the product of a perfect cube and the remaining number:

∛12 = ∛(2^2 × 3) = ∛(2^2) × ∛3 = 2 × ∛3

So, we can rewrite 3√12 as 3 × 2 × √3 = 6√3.

Step 2: Simplify the expression 10√3 - 6/√3.

Since we have a subtraction in the expression, we need to ensure that both terms have the same radical (√3). To do this, we need to rationalize the denominator of the second term.

To rationalize the denominator, we multiply the numerator and denominator of the fraction by the conjugate of the denominator, which is also √3.

6/√3 is equivalent to (6/√3) * (√3/√3) = 6√3 / 3 = 2√3.

Now, the expression becomes 10√3 - 2√3 = 8√3.

Step 3: Combine the simplified terms.

The expression 3√12 - (10√3 - 6/√3) becomes 6√3 - 8√3 = -2√3.

So, the final answer is -2√3.