Comparing irrational numbers with radicals

Introduction

Sometimes we run into numbers that can’t be written as simple fractions. These are called irrational numbers. Square roots, such as √2, and cube roots, such as ∛70, are examples. You’ll find irrational numbers when measuring diagonals, working with areas, or using t...

While doing homework, Jason saw a question: Which irrational number is greater, √35 or ∛80?

He starts by estimating nearby perfect squares and cubes.

Since 5² = 25 and 6² = 36, √35 is between 5 and 6.

For ∛80, 4³ = 64 and 5³ = 125. So, ∛80 is between 4 and 5.

This already shows...