What is the square root of 4.5?

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Answer 1 · 2015-09-15T10:17:13

#3/2 * sqrt(2)#

You know that

#4.5 = 45/10#

This means that you can write

#sqrt(4.5) = sqrt(45/10) = sqrt(45)/sqrt(10)#

Since #45 = 3 * 3 * 5#, you can write

#sqrt(45)/sqrt(10) = sqrt(3 * 3 * 5)/sqrt(10) = (3sqrt(5))/sqrt(10)#

Rationalize the denominator by multiplying the faction by #1 = sqrt(10)/sqrt(10)#

#(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))#