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.
Example 2
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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Example 3
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?
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, right?
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