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Simplify : 7 root 3 / root 10 + root 3 - 2 root 5 / root 6 + root 5 - 3 root 2 / root 15 + 3 root 2
4 months ago
Q:
simplify : 7 root 3 / root 10 + root 3 - 2 root 5 / root 6 + root 5 - 3 root 2 / root 15 + 3 root 2
Accepted Solution
A:
The answer is
-9β30 + 30β5 + 30β3 + 90β2
We first simplify all of the denominators by multiplying top and bottom by the radical:
(7β3/β10)(β10/β10) +Β β3 - (2β5/β6)(β6/β6) +Β β5 - (3β2/β15)(β15/β15) + 3β2
= 7β30/10 +Β β3 - 2β30/6 +Β β5 - 3β30/15 + 3β2
Multiply everything by 30 to simplify the fractions:
(7β30/10)(30) + 30β3 - (2β30/6)(30) + 30β5 - (3β30/15)(30) + 30*3β2
=210β30/10 + 30β3 - 60β30/6 + 30β5 - 90β30/15 + 90β2
Dividing we get
7β30 + 30β3 - 10β30 + 30β5 - 6β30 + 90β2
Combining like radicals we have
-9β30 + 30β3 + 30β5 + 90β2