Noam walks home from school by walking 8 blocks north and then 6 blocks east. how much shorter would his walk be if there were a direct path from the school to his house? assume that the blocks are square.

the distance he travels is 6+8=14 blocks. the straight line distance is the hypotenuse of a right triangle with legs 8 and 6.
6²+8³=c²
36+64=c²
100=c²
c= √100 = 10 blocks.