$($a$)$ Suppose a and $b$ are integers such that $a+b\sqrt[\phantom{2}]{2}=$

$3+5\sqrt[\phantom{2}]{2}.$ Prove that $a=3$ and $b=5.$

$($b$)$ Prove that $3+5\sqrt[\phantom{2}]{2}$ is not the square of a real number

of the form $a+b\sqrt[\phantom{2}]{2},$ where a and $b$ are integers.