Simplify: Sqrt(363) -3 * sqrt(27)
Step 1: Simplify the radicals inside the square roots.
sqrt(363) = sqrt(121 × 3) = sqrt(121) × sqrt(3) = 11sqrt(3)
sqrt(27) = sqrt(9 × 3) = sqrt(9) × sqrt(3) = 3sqrt(3)
Step 2: Substitute the simplified radicals back into the expression.
11sqrt(3) - 3 × 3sqrt(3)
Step 3: Multiply the coefficients (the numbers in front of the radicals) and subtract the resulting terms.
11sqrt(3) - 9sqrt(3)
Step 4: Combine like terms.
2sqrt(3)
Therefore, sqrt(363) -3 * sqrt(27) = 2sqrt(3)