# The sum of the squares of two positive numbers is 9,so how much will the sum of their cubes be??

May 24, 2018

$27$

#### Explanation:

${x}^{2} + {y}^{2} = 9$

What squares can add up to 9?

$0 + 9 = \sqrt{0} + \sqrt{3}$ Works!
$1 + 8$ Neither are perfect squares
$2 + 7$ Neither are perfect squares
$3 + 6$ Neither are perfect squares
$4 + 5$ Neither are perfect squares
now repeats...

so only ${0}^{2} + {3}^{2}$ works

${0}^{3} + {3}^{3} = 27$