2 answers

How do you simplify #5sqrt(12)+sqrt(75)#?

Question:

How do you simplify #5sqrt(12)+sqrt(75)#?

Answers

#15sqrt3#

Explanation:

Simplifying...

#sqrt75#

#-> sqrt25 xx sqrt 3#

#-> 5sqrt3#

Simplifying again:

#5sqrt12#

#-> 5 sqrt4 sqrt3#

#-> 5 xx 2sqrt3#

#-> 10sqrt3#

Adding terms:

#5sqrt3+10sqrt3#

Since the roots are the same, just add the numbers in front...

#-> 15sqrt3#

.

Given

#5sqrt12+sqrt75#

Factorizing numbers under the root sign we get

#5sqrt(2xx2xx3)+sqrt(3xx5xx5)#

Paring number which can be taken out of root sign

#5sqrt(bar(2xx2)xx3)+sqrt(3xxbar(5xx5))#
#=>5xx2sqrt(3)+sqrt(3)xx5#
#=>10sqrt(3)+5sqrt(3)#
#=>sqrt(3)(10+5)#
#=>15sqrt(3)#

.

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