N = 2a + b. a is a 2 digit square number, b is a 2 digit cube number. What is the smallest possible value of N?

First, the smallest values of a and b must be found and then substituted into the equation for N.

To find a.

A square number is a number that is the result of multiplying and number by itself . Eg 2 squared is (2*2) = 4 so 4 is a square number. 

The smallest value of a is the first 2 digit square number. This can be found by writing down the square numbers.

1 squared = 1

2 squared = 4

3 squared = 9

4 squared = 16

This shows that a is 16

To find b.

A cube number is a number that is the result of multiplying a number by itself twice. Eg 2 cubed is 222 = 8 so 8 is a square number. 

The smallest value of a is the first 2 digit cube number. This can be found by writing down the cube numbers.

1 cubed = 1

2 cubed = 8

3 cubed = 27

This shows that b is 27

Now we have the values for a and b we can put them int the original equation and find N.

N=2a+b

N=2*16 + 27

N = 59