Go step by step to reduce the radical.
square root of, 180, end square root
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square root of, empty space, end square root
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square root of, empty space, end square root
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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.
To simplify the square root of 180, you can break it down into its prime factors:
Step 1: Start by finding the prime factorization of 180:
180 = 2 * 2 * 3 * 3 * 5
Step 2: Group the prime factors into pairs:
2 * 2 * 3 * 3 * 5 = (2 * 2) * (3 * 3) * 5
Step 3: Take out the pairs of numbers from under the square root:
√((2 * 2) * (3 * 3) * 5) = 2 * 3 * √5
Step 4: Multiply the numbers outside the square root:
2 * 3 * √5 = 6√5
Therefore, the square root of 180 can be simplified to 6√5.
To simplify the square root of 180, follow these steps:
Step 1: Determine the prime factorization of the number inside the radical. Factors of 180 are 2, 2, 3, 3, and 5. So, we can write 180 as 2 * 2 * 3 * 3 * 5.
Step 2: Group pairs of factors. For every pair of identical factors, take one factor out of the square root. In this case, we have pairs of 2's and pairs of 3's. So, we can write the square root of 180 as the product of the factors taken out of the square root sign: 2 * 3 * square root of (2 * 3 * 5).
Step 3: Simplify the expression inside the square root. The remaining factors inside the square root are 2, 3, and 5. We multiply them together to get 30. So, the square root of (2 * 3 * 5) is the square root of 30.
Therefore, the simplified square root of 180 is 6 * square root of 30.
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.
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!