KnowledgeBoat Logo

Mathematics

Insert three irrational numbers between 232\sqrt{3} and 252\sqrt{5} , and arrange in descending order.

Rational Irrational Nos

6 Likes

Answer

Consider the squares of 232\sqrt{3} and 252\sqrt{5}.

(23)2(2\sqrt{3})^2 = 4 × 3 = 12 and (25)2(2\sqrt{5})^2 = 4 × 5 = 20

As , 18>17>1518 \gt 17 \gt 15 it follows that

18>17>15\sqrt{18} \gt \sqrt{17} \gt \sqrt{15} , therefore

18\sqrt{18} , 17\sqrt{17} , 15\sqrt{15} lie between 12\sqrt{12} and 20\sqrt{20} i.e. 232\sqrt{3} and 252\sqrt{5}.

Hence, three irrational number between 232\sqrt{3} and 252\sqrt{5} in descending order are 18\sqrt{18} , 17\sqrt{17} , 15\sqrt{15}.

Answered By

3 Likes


Related Questions