Which of the following describes the positive solution to the equation below?
the solution is an irrational number.
the solution is a rational number.
the solution is greater than two but less than three.
the solution is a repeating decimal.
the solution is greater than one but less than two.
the solution is greater than zero but less than one.
choose all that apply

The solution is an irrational number ⇒ 1st answer

The solution is greater than two but less than three ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some definitions

- A number is rational if we can write it as a fraction where the numerator

 and the denominator are both whole numbers

- A number is irrational if cannot be written as a ratio of two integers

- Repeating decimals are rational numbers because they can be

 represented as a ratio of two integers

* Lets solve the problem

- The equation is x² = 5

- To solve the equation take square root for both sides

∴ x = ± √5

∵ We need the positive solution

∴ x = √5

∵ √5 cannot be written as a ratio of two integers

∴ √5 is an irrational number

∴ The solution is an irrational number

- To find between which two integers √5 lies, find the two square

  numbers before and after 5

∵ 4 is a square number less then 5

∵ 9 is a square number greater than 5

∴ 4 < 5 < 9 ⇒ take square root for all

∴ √4 < √5 < √9

∵ √4 = 2 and √9 = 3

∴ √5 lies between 2 and 3 ⇒ 2 < √5 < 3

∴ The solution is greater than two but less than three

a

step-by-step explanation: