Sign In
Recall the definitions of square roots and cube roots.
See solution.
We are asked to give some examples of situations in which we would use square roots and cube roots. Let's do it!
Imagine a square lot with an area of 144 square meters. We want to cover the lot with rolls of grass. For that, we need to find the side length of the lot.
Let a be the length of the side. We know that the area of a square is its side squared. This tells us that a^2 is 144 square meters.
Now, to find a, we need to find the square root of 144. a^2 = 144 ⇔ a = sqrt(144) A square root of 144 is one of its two equal factors. In this case 144 = 12^2, which tells us that sqrt(144) = 12. This gives us the value of a. sqrt(144) = 12 ⇒ a = 12 The side of the lot is 12 meters.
If an airplane increases its speed some number of times, the drag of the airplane increases that number cubed. For example, if the speed of a plane increased 1.5 times, then the increase in the drag is ( 1.5)^3 = 3.375 times than it was before.
Let x be the increase in speed. We know that the drag of the airplane increased 8 times. We want to find x. Let's write what we know so far. x^3 = 8 If we take the cube root of both sides of the equation, this is what we get. x^3 = 8 ⇒ x = sqrt(8) We know that 8 is a perfect cube because 8 = 2^3. This tells us that sqrt(8)=2. sqrt(8)=2 ⇒ x = 2 We found that the airplane increased its speed 2 times.
