Question

Help!

which sum is rational?

A.)

`\pi + 18`
B.)

`√(25 + 1.75)`
C.

`√(3 + 5.5)`
D.)

`\pi + √(2)`

Answer 1

`\pi+18-irrational\ because\ \pi\ is\ irrational\\\\√(25+1.75)=√(26.75)=\sqrt{(2675)/(100)}=(√(2675))/(√(100))=(√(25\cdot107))/(10)\\\\=(√(25)\cdot√(107))/(10)=(5√(107))/(10)=(√(107))/(2)-irrational\\\\√(3+5.5)=√(8.5)=\sqrt{(85)/(10)}=\sqrt{(850)/(100)}=(√(850))/(√(100))=(√(25\cdot34))/(10)\\\\=(√(25)\cdot√(34))/(10)=(5√(34))/(10)=(√(34))/(2)-irrational`

`\pi+\sqrt2-irrational`