Can someone show me how to Simplify the radical expression
�ã363-3�ã27
in steps please
To simplify the radical expression �ã363-3�ã27, follow the steps below:
Step 1: Simplify the radicals individually.
First, simplify the radical �ã363. To do this, determine the factors of 363. Factors of 363 are 3 and 121. Since 121 is a perfect square, it can be written as 11^2. The square root of 363 can be expressed as the product of the square root of its perfect square factor and the square root of the remaining factor:
�ã363 = �ã(3×121) = �ã(3×11^2) = �ã3×�ã11^2 = �ã3×11 = 11�ã3
Next, simplify the radical �ã27. Identify the factors of 27. Factors of 27 are 3 and 9. Since 9 is a perfect square, it can be written as 3^2. The square root of 27 can be expressed as the product of the square root of its perfect square factor and the square root of the remaining factor:
�ã27 = �ã(3×9) = �ã(3×3^2) = �ã3×�ã3^2 = �ã3×3 = 3�ã3
Step 2: Combine the simplified radicals.
Now, substitute the simplified radicals back into the original expression:
11�ã3 - 3�ã3
Step 3: Combine like terms.
Since both terms have the same radical, which is �ã3, they can be combined by adding or subtracting the coefficients in front of the radical:
11�ã3 - 3�ã3 = (11 - 3)�ã3 = 8�ã3
Therefore, the simplified form of the original expression �ã363-3�ã27 is 8�ã3.