Find the geometric mean of 3 and 13. Leave your answer in simplest radical form!
Show work.
The geometric mean of two numbers is the square root of their product.
So, the geometric mean of 3 and 13 is:
√(3*13)
= √39
Therefore, the geometric mean of 3 and 13 is √39.
To find the geometric mean of two numbers, you need to multiply them together and then take the square root.
Step 1: Multiply the two numbers together.
3 * 13 = 39
Step 2: Take the square root of the product.
√39
So, the geometric mean of 3 and 13 is √39 in simplest radical form.
To find the geometric mean of two numbers, we need to take the square root of their product.
The product of 3 and 13 is 39.
Therefore, the geometric mean of 3 and 13 is the square root of 39.
To simplify the square root of 39, we need to find the largest perfect square that divides evenly into 39. The largest perfect square that divides evenly into 39 is 9.
We can write 39 as 9 * 4 + 3, which means 39 can be expressed as 9 plus a remainder of 3.
Thus, we can write the square root of 39 as the square root of (9 * 4 + 3), which is the square root of (3^2 * 4 + 3).
Taking out the perfect square factor, we can rewrite the square root of 39 as 3 * the square root of 4 + the square root of 3.
Therefore, the geometric mean of 3 and 13 is 3 * the square root of 4 + the square root of 3.