00:00The geometric mean of A and B is 56, the geometric mean of B and C is 7, and the geometric mean of A and C is...
00:0428.
00:05The question asks what the geometric mean of numbers A and C is, given the given information.
00:09Friends, if the geometric mean of A and B is 56, then there are two numbers.
00:13Now we say the square root of AB equals 56.
00:16We say that the square root of BC equals 7.
00:20We say that the square root of A times C equals 28.
00:25If we multiply these side by side, we can do so because they all have the same square root inside them.
00:31A squared times B squared times C squared equals 56 times 7 times 28.
00:39Okay guys, isn't that 56 times 7 times 8?
00:41Yes, 7 times 8 times 7 times 7 times 4.
00:45Now, what we're going to do here, guys, I'll tell you, but first, let's get rid of these things completely.
00:51A times B times C, which equals 7 cubed times 8, what is that, friends? 2 cubed times 4.
00:59What do we need now?
01:00To find the geometric mean of the numbers ABC, we need to take the cube root of their mean.
01:05The cube root of A times B times C, and substituting this into the square root of 7 cubed times 2.
01:12The cube of multiplied by 4 is equal to .
01:15The cube root cancels out, the cube root cancels out again, so we get 14 multiplied by the cube root of 4.
01:24The answer is Adana 14 cube root 4.
01:28Translation and Subtitles by M.K.
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