3square root of 18 + 3 square root of 12 + 2square root of 27 =
3√18 + 3√12 + 2√27
= 9√2 + 6√3 + 6√3
= 9√2 + 12√3
-3square root of 2+ 3square root of 20-3square root of 8
18= 2x3x3
12=2x2x3
27=3x3x3
3√2x3x3+3√2x2x3+2√3x3x3
3x3√2+3x2√3+2x3√3
9√2 + 6√3 + 6√3
9√2 + 12√3
-2√20 + 2√18 - 2√5
To simplify the expression 3√18 + 3√12 + 2√27, we need to find the simplified values of the square roots.
First, let's break down the numbers under the square roots into their prime factors:
√18 = √(2 * 3 * 3) = √(2^1 * 3^2)
√12 = √(2 * 2 * 3) = √(2^2 * 3)
√27 = √(3 * 3 * 3) = √(3^3)
Now, we can simplify each square root:
√(2^1 * 3^2) = √(2^1) * √(3^2) = √2 * 3 = 3√2
√(2^2 * 3) = √(2^2) * √3 = 2 * √3 = 2√3
√(3^3) = 3√3
Now we substitute the simplified values back into the expression:
3√18 + 3√12 + 2√27 = 3(3√2) + 3(2√3) + 2(3√3)
= 9√2 + 6√3 + 6√3
= 9√2 + 12√3
Therefore, the simplified expression is 9√2 + 12√3.