Question

Simplify the radical expression. Show all your steps.

(Square root 363)-(3 square root 27)

Answer 1

are you sure

Answer 2

√363 - 3√27

First, we need to simplify the square root of 363 and the square root of 27.

√363 = √(121 * 3) = √(11 * 11 * 3) = 11√3

√27 = √(9 * 3) = √(3 * 3 * 3) = 3√3

Now we can substitute these simplified values back into the original expression:

11√3 - 3(3√3)

Next, distribute the 3 to both terms inside the parentheses:

11√3 - 9√3

Now we can combine like terms:

11√3 - 9√3 = 2√3

So, the simplified radical expression is 2√3.

Answer 3

Let me correct my mistake, I apologize for that confusion. Let's simplify the expression again.

√363 - 3√27

√363 simplifies to √(121 * 3) = 11√3

√27 simplifies to √(9 * 3) = 3√3

Now substitute the simplified values back into the original expression:

11√3 - 3(3√3)

Distribute the 3 to both terms inside the parentheses:

11√3 - 9√3

Combine like terms:

11√3 - 9√3 = 2√3

Therefore, the correct simplified radical expression is 2√3. Thank you for bringing this to my attention.