Question

Find the geometric mean of each pair of numbers.

26. √8 and √2 (This is the one I'm having troubles with because the square root symbol is already on the numbers.)

I want to make sure I'm doing the others right too, so I want someone to double check my work for a few of them.

12. 4 and 10
x=√4x10
x=√4 x √10
x=2√10

14. 5 and 125
x=√5x125
x=√5x5x25
x=√25 x √25
x=5x5
x=25

Answer 1

Well, to find the geometric mean, you multiply the numbers together, and then find the square root of both. So, to multiply two numbers in radicals, you just keep them under the radical and multiply them together. Since 8 times two is 16, root 8 times root 2 is root 16. To square a square root, you simply just take away the square root, so the answer would be 16.
The other two problems are correct. Good job!

Answer 2

Right, @neonumbrella1234?

Answer 3

Thank you! That helped a lot.

Answer 4

No problem!
Glad I could help!

Answer 5

If the geometric mean of two numbers a, c is b then a,b,c are in geometric progression.
Which means b/a = c/b. hence b**2 (b raised to power 2)=a x c. Then b is called Geometric mean.
Hence if b**2 =a x c then b = sqrt(a x c)
In the problem a= sqrt(8), c = sqrt(2)
Hence GM(geometric mean) = sqrt (sqrt(8) X sqrt(2)) = sqrt(sqrt(16))= sqrt(4) = 2