Answer:
The solution is an irrational number ⇒ 1st answer
The solution is greater than two but less than three ⇒ 3rd answer
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