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.
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.
3 answers
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 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.
2 answers