Find the geometric mean of each pair of numbers.
1/12, 1/18
I understand to multiply 1/12 * 1/18 and take the sqrt of the answer. But, what would be the sqrt of (1/288)?
-18, -36 I got 25.46 for my answer.
Geometric Mean is the nth root of the
product of a set of numbers. So when
there's 2 numbers, take the square root
of the product. When there's 3 numbers,
take the cube root of the product and so on.
1. sqrt(1/12*1/18) = sqrt(1/216) = 1/14.697 = 0.06804.
2. 25.46 is correct.
To find the square root of a number, you can use a calculator or a mathematical technique called "prime factorization." I will explain both methods.
Method 1: Using a Calculator
To find the square root of a number, you can use a calculator that has a square root function.
In your case, the number is 1/288. Enter this number into your calculator and use the square root function to find the answer. The square root of 1/288 is approximately 0.0913.
Method 2: Prime Factorization
To find the square root of a number using prime factorization, follow these steps:
1. Prime factorize the number inside the square root. In this case, the number is 1/288. Since both 1 and 288 are perfect squares, their prime factorizations are:
1 = 1
288 = 2^5 * 3^2
2. Split the prime factors into two groups, with each factor appearing once in each group. The number of factors in each group should be equal or differ by one. In this case, we can split the prime factors as:
Group 1: 2^5 * 3^1 (has 6 factors)
Group 2: 2^0 * 3^1 (has 2 factors)
3. Take the product of each group. In this case, the product of Group 1 is (2^5 * 3^1) = 96, and the product of Group 2 is (2^0 * 3^1) = 3.
4. Take the square root of both products. The square root of 96 is approximately 9.798, and the square root of 3 is approximately 1.732.
5. Finally, multiply the square roots of the two products to get the square root of the original number. In this case, (9.798 * 1.732) is approximately equal to 16.945.
Therefore, the square root of 1/288 is approximately 16.945.