simplify.
3√12 + 5√3 - 3^√24
To simplify this expression:
Step 1: Simplify the square roots:
√12 = 2√3 (since 12 can be factored as 4 * 3 and 4 is a perfect square)
√24 = 2√6 (since 24 can be factored as 4 * 6 and 4 is a perfect square)
Step 2: Rewrite the expression with the simplified square roots:
3√12 + 5√3 - 3^√24 = 3(2√3) + 5√3 - 3(2√6)
Step 3: Simplify the coefficients:
3(2√3) = 6√3
3(2√6) = 6√6
Step 4: Combine like terms:
6√3 + 5√3 - 6√6
Step 5: Combine like terms again:
(6√3 + 5√3) - 6√6 = 11√3 - 6√6
So, the simplified expression is 11√3 - 6√6.