How to solve this problem √363−3√27
Need step by step instructions.
Thanks,
Kaai97
factor both:
363=3*121=3*11^2
27=3^2 * 3
√363−3√27 =
11sqrt3+3*3sqrt3
(11+9)sqrt3
20sqrt3
To solve the problem √363−3√27, follow these step-by-step instructions:
Step 1: Simplify the square root of 27
- The square root of 27 can be simplified by breaking it down into its prime factors.
- Since 27 = 3 × 3 × 3, the square root of 27 can be simplified as follows:
√27 = √(3 × 3 × 3) = 3√3
Step 2: Substitute the simplified value of the square root of 27 into the equation
- Replace the square root of 27 in the original equation with its simplified value:
√363 − 3(3√3)
Step 3: Simplify the square root of 363
- The square root of 363 can also be simplified by breaking it down into its prime factors.
- Since 363 = 3 × 11 × 11, the square root of 363 can be simplified as follows:
√363 = √(3 × 11 × 11) = 11√3
Step 4: Substitute the simplified value of the square root of 363 into the equation
- Replace the square root of 363 in the equation with its simplified value:
11√3 − 3(3√3)
Step 5: Combine like terms
- Multiply the coefficient outside the parentheses (3) with the value inside the parentheses (3√3):
11√3 − 3 × 3√3 = 11√3 − 9√3
Step 6: Simplify the expression
- Subtract the simplified values of the square roots:
11√3 − 9√3 = (11−9)√3 = 2√3
Therefore, the solution to the equation √363−3√27 is 2√3.
To solve the problem √363 - 3√27, we will break down the steps into simpler parts. First, let's simplify the square root of 363.
Step 1: Simplify the square root of 363:
Start by finding the prime factorization of 363. Divide it by its factors until you have only prime numbers left.
Prime factorization of 363:
363 ÷ 3 = 121
121 ÷ 11 = 11
11 is a prime number, so we stop here.
Now, rewrite 363 using its prime factorization:
363 = 3 * 11 * 11
Step 2: Simplify the square root of 363:
Since 363 contains a perfect square factor (11 * 11), we can simplify the square root:
√363 = √(3 * 11 * 11) = 11√3
Now, let's simplify the square root of 27.
Step 3: Simplify the square root of 27:
Find the prime factorization of 27:
27 ÷ 3 = 9
9 ÷ 3 = 3
3 is a prime number, so we stop here.
Now, rewrite 27 using its prime factorization:
27 = 3 * 3 * 3
Step 4: Simplify the square root of 27:
Since 27 contains a perfect square factor (3 * 3 * 3), we can simplify the square root:
√27 = √(3 * 3 * 3) = 3√3
Now, substitute the simplified square roots back into the original problem:
√363 − 3√27 = 11√3 - 3(3√3)
Step 5: Simplify the expression:
Multiply 3 and 3√3:
11√3 - 3(3√3) = 11√3 - 9√3
Combine like terms:
11√3 - 9√3 = (11 - 9)√3 = 2√3
Therefore, the simplified form of √363 − 3√27 is 2√3.