Find the two square roots of four-ninths.
Squaring a number and finding a square root are inverse operations. So if you’re trying to find the square root of a number, you’re actually gonna be finding the number that you square, in order to get that number.
When we look at four-ninths and we find the square root of four-ninths, we can find the square root of four and the square root of nine separately. The square root of four is actually two. The reason is, four is equal to two squared. And since squaring a number and finding a square root are inverse operations, they cancel each other.
So all we have left is two. Now let’s look at the square root of nine. Nine is actually three squared, three times three. And taking the square root of three squared will eliminate the square in a radical sign. The radical sign is that square root symbol. So the square root of nine is three. So the square root of four-ninths is two-thirds. Now it says to find two square roots of four-ninths. The reason is because when you square a positive number, you get a positive. And if you square a negative number, you also get a positive.
So two-thirds and negative two-thirds are the two square roots of four-ninths. To check our work, let’s square each and make sure we get four-ninths.
If we square two-thirds, two squared is two times two, which is four, and three squared is three times three, which is nine. So we get four-ninths.
Negative two-thirds, we can move the negative sign up with the two instead of out front. So now we’re gonna square it. So now negative two squared will be negative two times negative two, and three squared will be three times three. So on the numerator, negative two times negative two is positive four. And three times three is nine. Therefore, the two square roots of four-ninths is two-thirds and negative two-thirds.