How do you evaluate #\sqrt { 180} \cdot ( 2^- 2)#?

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Answer 1 · 2017-12-10T09:39:23

#color(blue)((3sqrt(5))/2)#

We are given the radical expression

#color(red)(sqrt(180)*2^-2)# #color(blue)(Expression.1#

Consider #sqrt(180)# for simplification

Note that we can write #sqrt(180)# as #sqrt(4*45)#

Next we can write #sqrt(4*45)# as #sqrt(4)*sqrt(45)#

#rArr 2sqrt(45)#

#rArr 2sqrt(9*5)#

#rArr 2sqrt(9)*sqrt(5)#

#rArr 2*3*sqrt(5)" "# ...Result.1

Now, using our intermediate result ...Result.1 we can write our #color(blue)(Expression.1# as

#(2*3*sqrt(5))/2^2# using the formula #color(green)(m^-n = 1/m^n)#

#rArr(2*3*sqrt(5))/(2*2)#

#rArr(cancel2*3*sqrt(5))/(cancel2*2)#

#color(blue)(rArr(3sqrt(5))/2)#

I hope you find this solution process useful.