Question%0D%0A%0D%0AWatch Video%0D%0A%0D%0AShow Examples%0D%0AGo step by step to reduce the radical.%0D%0Asquare root of, 180, end square root %0D%0A180%0D%0A%E2%80%8B%0D%0A %0D%0Asquare root of, end square root %0D%0Ax%0D%0A%E2%80%8B%0D%0A square root of, end square root %0D%0Ax%0D%0A%E2%80%8B%0D%0A try%0D%0AAnswer%0D%0AAttempt 1 out of 2%0D%0AYou must answer all questions above in order to submit.
To reduce the radical, you need to find the prime factorization of the number inside the radical. Let's go step by step.
Step 1: Prime factorize 180.
180 = 2^2 * 3 * 5^1
Step 2: Group the prime factors in pairs and take them out of the radical.
√(2^2 * 3 * 5) = 2 * √(3) * √(5)
Step 3: Simplify the radical.
√(3) * √(5) = √(3 * 5) = √15
So, the simplified radical form of √180 is √15.
For the second question, it seems like you didn't provide any number. Please specify the value of x so that we can proceed with the simplification.
can you break down the first step for me
Certainly! Let's break down the first step of finding the prime factorization of 180:
To find the prime factorization of a number, you need to determine which prime numbers can be multiplied together to give the original number as a product.
1. Start by dividing the number by the smallest prime number, which is 2. In this case, 180 is divisible by 2, so we can factor it out.
180 ÷ 2 = 90
2. Now, we divide the resulting quotient, 90, by 2 again.
90 ÷ 2 = 45
3. Repeat this process of dividing by 2 until the quotient is no longer divisible by 2.
45 ÷ 2 = 22.5 (not divisible by 2)
Since 45 is not divisible by 2, we move on to the next prime number, which is 3.
4. Divide 45 by 3.
45 ÷ 3 = 15
5. Continue dividing by prime numbers until the quotient is no longer divisible.
15 ÷ 3 = 5
6. Finally, divide the remaining quotient, 5, by the next prime number, which is 5.
5 ÷ 5 = 1
By this point, we have reached 1, and we cannot divide it any further.
Therefore, the prime factorization of 180 is:
180 = 2^2 * 3 * 5^1
I hope that helps! Let me know if you have any further questions.
To reduce the radical of a number, such as the square root of 180, you can start by checking if the number inside the radical has any perfect square factors. In this case, 180 can be factored as 2^2 * 3^2 * 5.
To simplify the square root of 180, you can take out the perfect square factors from inside the radical. The perfect square factors are 2^2 and 3^2, which can be taken outside the radical as 2 * 3.
The simplified form of the square root of 180 is 2 * 3 * square root of 5, which can be written as 6 * square root of 5.
So, the simplified expression is: square root of 180 = 6 * square root of 5.