Find the geometric mean of the pair of numbers below. If necessary, give the answer in simplest radical form.
5 and 18
For any two numbers A and B, their geometric mean is given by √(AB)
In this case, A = 5, B = 18
=> G.M. = √(5*18)
= √90
= 3√10
To find the geometric mean of a pair of numbers, you need to multiply the two numbers and then take the square root of the result.
In this case, the pair of numbers is 5 and 18. So, you multiply 5 and 18 together:
5 * 18 = 90
Then, you take the square root of 90.
To simplify the square root, you can look for perfect square factors. In this case, the largest perfect square factor of 90 is 9. So, you can rewrite 90 as 9 * 10.
√(9 * 10)
You can then take the square root of the perfect square factor, which is 3:
3√10
Therefore, the geometric mean of 5 and 18 is 3√10.