First step: Find out the prime numbers that make up the radical, for example, 120 would be 2x2x2x5x3
Second step: If there is 2 of the same number that repeats just put that number in the front of the resulting radical
Third: Just multiply the remaining radicals together and put the number in front of it.
Now you have
Answer:
78 0: )
Step-by-step explanation:
Ratio of their volumes = a³ : b³
Ratio of their surface areas =
<u>Step-by-step explanation:</u>
Two square pyramids are similar with their edges are in the ratio of a : b.
Volume of a square pyramid with edge and h = a is given by the formula,
= 
= 
Volume of a square pyramid with edge b and h = b is given by the formula,
= 
= 
Ratio of their volumes = a³ : b³ since h/3 gets cancelled.
Total surface area of square pyramid with the edge a =
Total surface area of square pyramid with the edge b =
Ratio of the surface area =
which tells you that the only critical point of
occurs at (2, 1), which does lie within the region
. At this point, we get
.
Next we check along the boundaries of
. They are the lines
with
,
with
, and
with
.
If
, then
, which is monotonically decreasing and must therefore attain its maximum at
and minimum at
. We get
and
.
If
, then
, which is also monotonically decreasing and attains its maximum at
and minimum at
. We get
and
.
If
, then
. We have
, which suggests an extremum occurs at (3, 2). We get
.
So
has a minimum value of 4 at (1, 4) and (5, 0), and a maximum value of 8 at (1, 0) and (3, 2).
