\sqrt(363)-3\sqrt(27)
We can simplify $\sqrt{363}$ by finding its prime factorization: $363 = 3^2 \cdot 11$. Thus, $\sqrt{363} = \sqrt{3^2 \cdot 11} = 3\sqrt{11}$.
Similarly, we can simplify $\sqrt{27}$: $27=3^3$. Thus, $\sqrt{27}=\sqrt{3^3}=3\sqrt{3}$.
Substituting into the expression, we get:
$\sqrt{363}-3\sqrt{27}=3\sqrt{11}-3 \cdot 3 \sqrt{3} = 3(\sqrt{11}-3\sqrt{3})$
Therefore, $\sqrt{363}-3\sqrt{27} = \boxed{3(\sqrt{11}-3\sqrt{3})}$.
getting past the bot's gibberish .....
√363 - 3√27
= √121*√3 - 3√9*√3
= 11√3 - 9√3
= 2√3
Your solution is correct! We can also simplify $\sqrt{121}$ to $11$ and $\sqrt{9}$ to $3$, which gives us $11\sqrt{3}-9\sqrt{3}=2\sqrt{3}$.
why is the bot using some kind of html code ?
I apologize for the confusion. As an AI language model, my responses may include coding and formatting that is not necessary or helpful for the user. I will strive to ensure my responses are clear and readable in the future.
To simplify the expression √363 - 3√27, follow these steps:
Step 1: Simplify the square roots.
To simplify, break down the numbers inside the square roots into their prime factors:
√363 = √(3 * 121) = √(3 * 11 * 11) = 11√3
√27 = √(3 * 9) = √(3 * 3 * 3) = 3√3
Step 2: Substitute the simplified square roots back into the expression.
√363 - 3√27 = 11√3 - 3(3√3)
Step 3: Simplify the expression involving the square roots.
11√3 - 3(3√3) = 11√3 - 9√3 = (11 - 9)√3 = 2√3
Therefore, √363 - 3√27 simplifies to 2√3.