Question

so sánh

a,\(\sqrt{37}-\sqrt{15}\) và 2

b,\(\sqrt{24}+\sqrt{49}\) và 12

c,\(\sqrt{33}-\sqrt{17}\) và \(6-\sqrt{15}\)

Answer 1

\(\sqrt{37}-\sqrt{15};2\)

có \(\left(\sqrt{37}-\sqrt{15}\right)^2=37-2\sqrt{555}+15=52-2\sqrt{555}\)

\(2^2=4\)

xét \(52-2\sqrt{555}-4=48-2\sqrt{555}\)

SS:\(48;2\sqrt{555}\)

\(48^2=2304\)

\(\left(2\sqrt{555}\right)^2=2220\)

2304>2220=>\(\sqrt{37}-\sqrt{15}>2\)

Answer 2

và 12

\(\left(\text{√ 24 + √ 49 }\right)^2=24+28\sqrt{6}+49=73+28\sqrt{6}\)

\(12^2=144\)

xét \(144-73-28\sqrt{6}=71-28\sqrt{6}\)

SS:\(71;28\sqrt{6}\)

\(71^2=5041\)

\(\left(28\sqrt{6}\right)^2=4704\)

5041>4704=>\(12>\sqrt{24}+\sqrt{49}\)