We are asked to give some examples of situations in which we would use square roots and cube roots. Let's do it!

Example $1$

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 \Leftrightarrow a = 144

A square root of

144

is one of its two equal factors. In this case

144 = 12^{2},

which tells us that

144 = 12 .

This gives us the value of

a .

144 = 12 \Rightarrow a = 12

The side of the lot is

12

meters.

Example $2$

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 \Rightarrow x = 38

We know that

8

is a perfect cube because

8 = 2^{3} .

This tells us that

38 = 2 .

38 = 2 \Rightarrow x = 2

We found that the airplane increased its speed

2

times.

Example 1

Example 2

Example $1$

Example $2$

Exercise