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Mathematics

Write the following real numbers in descending order :

2,3.5,10,−52,523\sqrt{2}, 3.5, \sqrt{10}, -\dfrac{5}{\sqrt{2}}, {\dfrac{5}{2}}{\sqrt{3}}

Rational Irrational Nos

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Answer

Write all the numbers as square root under one radical :

2=23.5=12.2510=10−52=−252=−12.5523=25×34=754=18.75Since,18.75>12.25>10>2>−12.5⇒18.75>12.25>10>2>−12.5⇒523>3.5>10>2>−52\sqrt{2} = \sqrt{2} \\[1.5em] 3.5 = \sqrt{12.25} \\[1.5em] \sqrt{10} = \sqrt{10} \\[1.5em] {-\dfrac{5}{\sqrt{2}}} = - \sqrt{\dfrac{25}{2}} = -\sqrt{12.5} \\[1.5em] {\dfrac{5}{2}}{\sqrt{3}} = \sqrt{\dfrac{25 × 3}{4}} = \sqrt{\dfrac{75}{4}} = \sqrt{18.75} \\[1.5em] \text{Since} , 18.75 \gt 12.25 \gt 10 \gt 2 \gt - 12.5 \\[1.5em] \Rightarrow \sqrt{18.75} \gt \sqrt{12.25} \gt \sqrt{10} \gt \sqrt{2} \gt -\sqrt{12.5} \\[1.5em] \Rightarrow {\dfrac{5}{2}}{\sqrt{3}}\gt 3.5 \gt \sqrt{10} \gt \sqrt{2} \gt -\dfrac{5}{\sqrt{2}}

Hence, the given numbers in descending order are 523,3.5,10,2,−52\bold{\dfrac{5}{2}{\sqrt{3}}} , \bold{3.5} , \bold{\sqrt{10}} ,\bold{\sqrt{2}} , \bold{-\dfrac{5}{\sqrt{2}}}.

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