Roots Examples

What's the cube root of -125?

We need to find a number that, when multiplied by itself three times, equals negative 125. With a little computation magic and a whole lot of thinking about it, we find that 5 × 5 × 5 = 125.

But wait...that's positive, not negative.

We're pretty close, so let's try -5.

(-5) × (-5) × (-5) =
25 × (-5) =
-125

Now that's what we're talking about. The cube root of -125 is -5.

What's the value of the following expression?

We've got two different roots here. The first term is the cube root of 27. Since we know 3 × 3 × 3 = 27, the cube root is just 3.

In the second term, the square root of 16 is a number we multiply by itself to get 16. Hmm...4 × 4 = 16, so that square root is 4.

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Finish up with some classic subtraction.

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What's the value of ?

Ugh. That's one ugly expression. What we're really after is a number that we can multiply by itself to get that fraction inside the square root.

If it seems tricksy, just think about the denominator by itself for a sec. What's the square root of 25?

We know 5 × 5 = 25, so the square root of 25 is 5.

But hey, we can do the same thing with fractions. We know that , right?

Right. That means comes out to .