Question

Stabiliți care dintre următoarele numere sunt raționale
$d = \sqrt{961} \\ e = \sqrt{2601} \\ f = \sqrt{5184}$
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Answer 1

Răspuns:

d,e,f

Explicație pas cu pas:

d=√961=√(31²)=31 rațional

e=√2601=√(9*289)=3*17=51 rațional

f=√5184=√(4*4*4*81)=2*2*2*9=72 rațional

Answer 2

 

$\displaystyle\bf\\ a=\sqrt{729}=\sqrt{729}=\sqrt{81\cdot9}=\sqrt{3^4\cdot3^2}=\sqrt{3^6}=3^3=\boxed{\bf~27\in Q}\\\\ b=\sqrt{288}=\sqrt{32\cdot9}=\sqrt{2^5\cdot3^2}=2^2\cdot3\sqrt{2}=12\sqrt{2}\notin Q\\\\c=\sqrt{147}=\sqrt{3\cdot49}=\sqrt{3\cdot7^2}=7\sqrt{3}\notin Q\\\\d=\sqrt{961}=\sqrt{31^2}=\boxed{\bf~31\in Q}\\\\e=\sqrt{2601}=\sqrt{9\cdot289}=\sqrt{3^2\cdot17^2}=3\cdot17=\boxed{\bf~51\in Q}\\\\f=\sqrt{5184}=\sqrt{64\cdot81}=\sqrt{2^6\cdot3^4}=2^3\cdot3^3=8\cdot9=\boxed{\bf~72\in Q}$