# simplify: square root 4/9?

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how do you simplify the square root of 4 over 9

• √(4/9) = ± 2/3

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I’m going to use the notation sqrt() to indicate “square root of.” When you simplify a square root (aka a radical), you want try to split it into numbers where one of those numbers is a perfect square (namely, the largest possible perfect square). A perfect square, in case you don’t know, is a number that has an integer square root, like 1, 4, 9, 16, etc. For example, you could split 75 up as either 15*5 or 25*3, so sqrt(75) is equal to both sqrt(15)*sqrt(5) or sqrt(25)*sqrt(3) However, in the first example, you can’t simplify either radical or express them as integers, so writing sqrt(75) in that form is kind of pointless because it doesn’t simplify it at all, really. In the second case, sqrt(25) becomes 5, which simplifies the expression. Another example: Square root of 72: 72 = 36*2, and so sqrt(72) = sqrt(36)*sqrt(2) = 6*sqrt(2). This works because 36 is the largest perfect square that divides 72 evenly. You can you use 9 and 8, because 9 is another perfect square that goes into 72 evenly. You get 3*sqrt(8), which is fine, but it can be simplified further, because sqrt(8) = 2*sqrt(2). If you don’t use the largest possible perfect square, you get a simplified form, but not the most simplified form. So basically, if you want to simplify the square root of some number, look for the largest perfect square that divides that number evenly, and that should be one of the numbers you pick (the other number being what you get when you divide by that perfect square, of course). Oh, and if you can’t divide a number by a perfect square other than 1, then the square root of that number can’t be simplified. Hope that helps 😀

• Take the square root of both numbers: (square root of 4) over (square root of 9).

The square root of 4 = 2 and -2. The square root of 9 = 3 and -3.

So, the answer is ± 2/3

• Is 4 A Square Number

• √ (4/9) = ± 2/3

• Do the square root of 4 and 9 separately. So it equals: 2/3.

• The square root of any fraction can be written as the square root of the numerator over the square root of the denominator. √(x/y) = √x/√y

Therefore, √(4/9) = √4/√9 = 2/3

• 2/3

• do you mean sqrt ( 4 ) / 9 or sqrt ( 4 / 9 ) ??

Source(s): my brain

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