Question 1065269
There are multiple solutions, but the integer one will be a=9 and b=5
I want a perfect square + 44 to equal a perfect cube.
I can start with known perfect cubes, 1,8,27,125,216,343,512, and subtract 44 from them:-43,-36,-17,81,172,299,468.
The first three don't have real number squares, but the fourth is a perfect square, 9, and its square + 44=125, which is 5^3.
For 216, a^2= sqrt (172), and a^2+44=6^3.
For 10^2=100, b^3=144 and b= cube root of 144.