Question

Порiвняти вирази:

1. [2]\sqrt{5} i 3\sqrt{2} ;

2. [7]\sqrt{3} i \sqrt{61} .

Answer 1

$\displaystyle\bf\\1)\\\\2\sqrt{5} =\sqrt{2^{2} \cdot 5} =\sqrt{4\cdot 5} =\sqrt{20} \\\\3\sqrt{2} =\sqrt{3^{2} \cdot 2} =\sqrt{9\cdot 2}=\sqrt{18}\\\\\sqrt{20} > \sqrt{18}\\\\\boxed{\boxed{2\sqrt{5} > 3\sqrt{2} }}\\\\\\2)\\\\7\sqrt{3} =\sqrt{7^{2}\cdot 3 } =\sqrt{49\cdot 3} =\sqrt{147} \\\\\sqrt{147} > \sqrt{61} \\\\\boxed{\boxed{7\sqrt{3} > \sqrt{61} }}$