Simplify
the square root of 363 - 3 the square root of 27
do you mean
sqrt(363) - 3sqrt(27)?
sqrt (3 * 121) - 3 sqrt (9*3)
sqrt (3 * 11 * 11) - 9 sqrt (3)
11 sqrt (3) - 9 sqrt (3)
2 sqrt (3)
To simplify the expression √363 - 3√27, we can start by simplifying the square roots individually.
First, let's simplify the square root of 363. To do this, we need to find the prime factors of 363.
The prime factorization of 363 is: 3 x 121.
Since 121 is a perfect square (11 x 11), we can rewrite the square root of 363 as the square root of 3 x 11 x 11.
Using the properties of square roots, we can break down the square root into separate square roots:
√(363) = √(3 x 11 x 11) = √3 x √(11 x 11) = √3 x 11 = 11√3.
Now let's simplify the square root of 27.
The prime factorization of 27 is: 3 x 3 x 3.
Using the same properties of square roots, we can simplify the square root of 27:
√(27) = √(3 x 3 x 3) = √3 x √(3 x 3) = √3 x 3 = 3√3.
Now we can substitute these simplified square roots back into the original expression:
√363 - 3√27 = 11√3 - 3(3√3).
And further simplifying:
11√3 - 9√3 = (11-9)√3 = 2√3.
Therefore, the simplified form of √363 - 3√27 is 2√3.