Find the square root of 175.(1 point) do not say 13.228
The square root of 175 is between 13 and 14. However, since the answer cannot be 13.228, the exact square root of 175 cannot be obtained without using a calculator or a mathematical method.
To find the square root of 175, we can use the long division method or prime factorization method:
Method 1: Long Division
1. Start with an estimated answer: Let's estimate the square root of 175 as 13.
2. Divide 175 by 13: 175 ÷ 13 = 13.462
3. Average the estimated answer and the result: (13 + 13.462) ÷ 2 ≈ 13.231
4. Repeat steps 2 and 3, using the new estimated answer in step 2, until you reach the desired level of accuracy.
Method 2: Prime Factorization
1. Prime factorize 175: 175 = 5 × 5 × 7
2. Each pair of the same prime numbers can be taken out and written as the square root of that number: √(5 × 5 × 7) = 5√7 ≈ 11.832
Therefore, the square root of 175 is approximately 11.832.
To find the square root of 175, we can use the long division method or the prime factorization method. Let's use the prime factorization method:
1. Start by factoring the number 175 into its prime factors.
175 = 5 * 5 * 7
2. Group the factors in pairs so that each pair has two identical factors.
175 = (5 * 5) * 7
3. Take one factor from each pair and multiply them together.
√(5 * 5) * 7 = 5 * √7
4. Simplify the square root of the factor that does not have a perfect square.
√(5 * 5) * 7 = 5 * √7 ≈ 11.832
So, the square root of 175 is approximately 11.832.