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

$3/10 * sqrt(50) = 3/10 * sqrt(5^2 * 2) = 3/10 * 5 * sqrt(2) = color(green)(3/2 * sqrt(2))$