Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the radical expression. Show all your steps.
√363−3√27
19 - 3(5.2) = ?
√121*3 −3√9*3
√11*11*3 −9√3
11√3 −9√3
2 √3
patience, plug and chug
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To simplify the given radical expression √363 - 3√27, we can start by simplifying each radical term separately.
Step 1: Simplify √363.
To simplify the square root of 363, we need to find the largest perfect square that divides into 363 evenly. The largest perfect square that divides into 363 is 121 (11^2), as 363 ÷ 121 = 3 with no remainder.
So, we can rewrite √363 as √(121 × 3).
Now, using the property √(ab) = √a × √b, we can split the square root of the product:
√(121 × 3) = √121 × √3
The square root of 121 (√121) equals 11, so we have:
11√3
Step 2: Simplify 3√27.
To simplify the cube root of 27, we need to find the largest perfect cube that divides into 27 evenly. The largest perfect cube that divides into 27 is 3^3, as 27 ÷ 3^3 = 1 with no remainder.
So, we can rewrite 3√27 as 3√(3^3).
Now, using the property n√(a^b) = a^(b/n), we can simplify the cube root as:
3√(3^3) = 3 × 3^(3/3)
Since 3/3 equals 1, we have:
3 × 3^1 = 3 × 3 = 9
Therefore, 3√27 simplifies to 9.
Now, we can rewrite the given expression:
√363 - 3√27 = 11√3 - 3√27 = 11√3 - 9
So, the simplified radical expression is 11√3 - 9.