How are exponents and radicals used to present roots of real numbers

Explanation:

Roots of real numbers can be represented by radicals or by exponents.

First, I present some examples to show how exponents and radicals are related, and then generalize.

When you write 5² = 25, then 5 is the square root of 25.

And in general, if n is a positive integer and , then is the nth root of x.

Also, if n even (and positive)  and is positive, then   is the positive nth root of

Thus,

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

the answer is 62.8 cubic units