Answers
Explanation:
You know that
#4.5 = 45/10#
This means that you can write
#sqrt(4.5) = sqrt(45/10) = sqrt(45)/sqrt(10)#
Since
#sqrt(45)/sqrt(10) = sqrt(3 * 3 * 5)/sqrt(10) = (3sqrt(5))/sqrt(10)#
Rationalize the denominator by multiplying the faction by
#(3sqrt(5))/sqrt(10) * sqrt(10)/sqrt(10) = (3 * sqrt(50))/10#
This can be further simplified to
#3/10 * sqrt(50) = 3/10 * sqrt(5^2 * 2) = 3/10 * 5 * sqrt(2) = color(green)(3/2 * sqrt(2))#
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