Question

Find the geometric mean of the pair of numbers: 81 and 4.
Question 18 options:

a) 38

b) 23

c) 28

d) 18

Answer 1

take the square root of the product ...

Answer 2

the geoMean of a and b is: sqrt(ab)

Answer 3

@amistre64 is right you just need to take the square root and then poof you get the answer

Answer 4

Ok if you really want the answer, look at other questions with different examples to figure it out.

Answer 5

amistre told you how to do it.

find the square root of the product ( product means multiply the two numbers)

Answer 6

i dont know how to do that

Answer 7

can you multiply 81 and 4 ?

Answer 8

ive asked what the two numbers are but they wont tell me are the 81 and 4?

Answer 9

oh it is

Answer 10

81 x 4 is 324

Answer 11

yes, the sentence
Find the geometric mean of the pair of numbers: 81 and 4.

means use 81 and 4

now find the square root of 324

you should learn an important idea:

factor the number into prime factors, and look for pairs of numbers.

it is easiest if you start with 4*81 (don't multiply it out to get 324)
instead, factor 4 into 2*2 and 81 into 3*3*3*3
so you have
sqrt(2*2*3*3*3*3)

pull out pairs of numbers

Answer 12

ok

Answer 13

sqrt(2*2*3*3*3*3) = sqrt(2*2) * sqrt(3*3) * sqrt(3*3)
and
sqrt(2*2)= 2
sqrt(3*3)= 3
sqrt(3*3)= 3

Answer 14

im still lost a little

Answer 15

do you agree 324 = 2*2*3*3*3*3 ?

Answer 16

yes

Answer 17

do you know that
sqrt( A * A) = A

you can simplify two A's inside a square root by making them 1 A outside the square root

Answer 18

that rule works for
sqrt(2*2*3*3*3*3)

notice you can write that as
sqrt( (2*3*3) * (2*3*3) )
by writing the numbers as pairs
you can simplify that to
sqrt( (2*3*3) * (2*3*3) ) = 2*3*3

Answer 19

or you can say: for every pair inside the square root, I can take that pair out, and put one of the pair outside the square root

so : sqrt(2*2*3*3*3*3) = 2 sqrt(3*3*3*3)
we took out the 2*2 from inside, and put a single 2 on the outside

we can to that for the 3's also:
2 * 3* sqrt(3*3)
we took out 1 pair of 3's
we can take out the last pair of 3's
2*3*3*sqrt(1) = 2*3*3= 18

Answer 20

ok

Answer 21

or use a calculator on sqrt(324)

(but it would be good to be able to do it without a calculator)

Answer 22

the sqrt is 18

Answer 23

yes, that means the geometric mean of 4 and 81 is 18

Answer 24

ok Thanks :DD

Answer 25

i have 5 more questions can you help me with those also?