last year bob's age was a square number and next year it will be a cube number.How old is Bob now?
Bob is 26.
Last year he was 25 = 5^2
Next year he'll be 27 = 3^3
25
To solve this problem, we need to determine the current age of Bob.
Let's assume that the current age of Bob is "x" years.
According to the information given:
1. Last year, Bob's age was a square number.
This means that (x-1) is a perfect square. To find possible values of (x-1), we can calculate the square root of (x-1) and check if it is an integer.
2. Next year, Bob's age will be a cube number.
This means that (x+1) is a perfect cube. To find possible values of (x+1), we can calculate the cube root of (x+1) and check if it is an integer.
By combining the two conditions, we need to find a value of x that satisfies both conditions.
To do this, we can start by choosing different values for x (for example, starting from x = 1) and checking if both (x-1) and (x+1) are perfect squares and perfect cubes, respectively.
We can continue this process until we find a value of x that satisfies both conditions. Once we find such a value, that will be Bob's current age.