Question

Cho \(A=\sqrt{625}-\dfrac{1}{\sqrt{5}};B=\sqrt{576}-\dfrac{1}{\sqrt{6}}+1\)

Hãy so sánh A và B

Answer 1

\(A=\sqrt{625}-\dfrac{1}{\sqrt{5}}=25-\dfrac{1}{\sqrt{5}}\)

\(B=\sqrt{576}-\dfrac{1}{\sqrt{6}}+1=24-\dfrac{1}{\sqrt{6}}+1=25-\dfrac{1}{\sqrt{6}}.\)

Vì \(\sqrt{5}< \sqrt{6}\) nên \(\dfrac{1}{\sqrt{5}}>\dfrac{1}{\sqrt{6}}.\)

Từ (1), (2) và (3) suy ra \(A< B.\)

Answer 2

B<A

Answer 3

⇒A= 25-\(\dfrac{1}{\sqrt{5}}\)

B =\(\sqrt{576}\) - \(\dfrac{1}{\sqrt{6}}+1\)

⇒B = 24-\(\dfrac{1}{\sqrt{6}}+1\)

Hay: B = (24+1)-\(\dfrac{1}{\sqrt{6}}\)

⇒ B=25-\(\dfrac{1}{\sqrt{6}}\)

Vì: 25-\(\dfrac{1}{\sqrt{5}}\) > 25-\(\dfrac{1}{\sqrt{6}}\)

Vậy: A > B