a) Z twierdzenia Pitagorasa:

$4^2+{\left(2\sqrt{5}\right)}^2=a^2$  

$16+4\cdot 5=a^2$  

$16+20=a^2$  

$36=a^2$  

$a=6$  

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b) Z twierdzenia Pitagorasa:

$2^2+b^2={\left(\sqrt{13}\right)}^2$  

$4+b^2=13$  

$b^2=9$  

$b=3$  

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c) Z twierdzenia Pitagorasa:

$c^2+{\left(3\sqrt{2}\right)}^2={\left(4\sqrt{2}\right)}^2$  

$c^2+9\cdot 2=16\cdot 2$  

$c^2+18=32$  

$c^2=14$  

$c=\sqrt{14}$  

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d) Z twierdzenia Pitagorasa:

${\left(\sqrt{3}\right)}^2+d^2={\left(1+\sqrt{2}\right)}^2$  

$3+d^2=1+2\sqrt{2}+2$  

$3+d^2=3+2\sqrt{2}$  

$d^2=2\sqrt{2}$  

$d=\sqrt{2\sqrt{2}}$  

$d=\sqrt{\sqrt{8}}$  

$d=\sqrt[4]{8}$