To reduce the square root of 180, we need to find the largest perfect square that divides evenly into 180.
1. First, let's list the prime factors of 180: 2, 2, 3, 3, 5.
2. Now, we can pair up the prime factors in twos: 2 × 2 × 3 × 3 × 5.
3. Next, we take one factor from each pair outside of the square root: 2 × 3 × sqrt(5).
4. Finally, we multiply the factors outside of the square root to simplify: 6 × sqrt(5).
So, the simplified radical of 180 is 6 times the square root of 5.
Go step by step to reduce the radical.
square root of, 180, end square root
180
square root of, empty space, end square root
x
square root of, empty space, end square root
x
5 answers
sorry but can you do it step by step please i forgot to specify.
Of course! Here are the step-by-step instructions to simplify the square root of 180:
Step 1: Start by finding the prime factorization of 180:
The prime factorization of 180 is 2 * 2 * 3 * 3 * 5.
Step 2: Group the prime factors into pairs:
(2 * 2) * (3 * 3) * 5.
Step 3: Take out the pairs of numbers from under the square root:
The square root of (2 * 2) is 2, and the square root of (3 * 3) is 3. So, we can take these numbers outside of the square root.
Step 4: Simplify the expression inside the square root:
We are left with the number 5 inside the square root.
Step 5: Multiply the numbers outside the square root:
The numbers outside the square root are 2 and 3. So, we can multiply them together to get 6.
Step 6: Combine the numbers inside and outside the square root:
The simplified form of the square root of 180 is 6 * square root of 5.
So, the square root of 180 can be simplified to 6 times the square root of 5.
Step 1: Start by finding the prime factorization of 180:
The prime factorization of 180 is 2 * 2 * 3 * 3 * 5.
Step 2: Group the prime factors into pairs:
(2 * 2) * (3 * 3) * 5.
Step 3: Take out the pairs of numbers from under the square root:
The square root of (2 * 2) is 2, and the square root of (3 * 3) is 3. So, we can take these numbers outside of the square root.
Step 4: Simplify the expression inside the square root:
We are left with the number 5 inside the square root.
Step 5: Multiply the numbers outside the square root:
The numbers outside the square root are 2 and 3. So, we can multiply them together to get 6.
Step 6: Combine the numbers inside and outside the square root:
The simplified form of the square root of 180 is 6 * square root of 5.
So, the square root of 180 can be simplified to 6 times the square root of 5.
im kinda confused witch ones are the sqare roots
Apologies for any confusion. Let me clarify which steps involve the square root symbol.
1. The prime factorization of 180 is 2 * 2 * 3 * 3 * 5.
2. Group the prime factors into pairs: (2 * 2) * (3 * 3) * 5.
3. Take out the pairs of numbers from under the square root: √(2 * 2) * √(3 * 3) * √5.
4. Simplify the expression inside the square root: √(2 * 2) = 2 and √(3 * 3) = 3. So we have 2 * 3 * √5.
5. Multiply the numbers outside the square root: 2 * 3 = 6.
Combining the results, the simplified form of the square root of 180 is 6√5.
I hope this clarifies the steps for you. Let me know if you have any further questions!
1. The prime factorization of 180 is 2 * 2 * 3 * 3 * 5.
2. Group the prime factors into pairs: (2 * 2) * (3 * 3) * 5.
3. Take out the pairs of numbers from under the square root: √(2 * 2) * √(3 * 3) * √5.
4. Simplify the expression inside the square root: √(2 * 2) = 2 and √(3 * 3) = 3. So we have 2 * 3 * √5.
5. Multiply the numbers outside the square root: 2 * 3 = 6.
Combining the results, the simplified form of the square root of 180 is 6√5.
I hope this clarifies the steps for you. Let me know if you have any further questions!
3 answers