How do you simplify: the square root of 4/9?

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Answer 1 · 2015-07-23T22:27:51

You take the square root of the denominator and of the numerator.

Start by writing out your initial expression

#sqrt(4/9)#

If you use the quotient property of radicals, you can write this expression as

#sqrt(4/9) = sqrt(4)/sqrt(9)#

Now, sicne both #4# and #9# are perfect squares

#4 = 2 * 2 - 2""^2#

#9 = 3 * 3 = 3""^2#

all you have to do is take the square root of both these numbers to get

#sqrt(4)/sqrt(9) = sqrt(2""^2)/sqrt(3""^2) = color(green)(2/3)#