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This is the second of our many quizzes on order real numbers. Click on this to access more such competitive quizzes on real numbers.

Order Real Numbers Quiz 2

mathematics

 Which of the following will be largest among the given numbers.

 Convert all the numbers in decimal form, then compare the decimal value of given terms.

  $\text{The decimal representation will be,} \\  \Rightarrow 4\sqrt 5  = (4 \times 2.23) \approx 8.92 \\  \Rightarrow \sqrt {20}  \approx 4.47 \\ \Rightarrow \dfrac{{\sqrt {40} }}{2} \approx \dfrac{{6.32}}{2} \approx 3.16 \\ \Rightarrow 2\sqrt {10}  \approx (2 \times 3.16) \approx 6.32 \\ \text{Hence, }4\sqrt 5\text{ has the highest value among all.}$

 Which of the following will be the correct order of arrangement?

  $\text{The decimal representation will be,}\\  - 4\sqrt 5  \approx  - (4 \times 2.23) \approx  - 8.92 \\ - \sqrt {20}  \approx  - 4.47 \\ - \dfrac{{\sqrt {80} }}{4} \approx  - \dfrac{{8.944}}{4} \approx  - 2.236 \\ - 3\dfrac{2}{5} =  - \dfrac{{17}}{5} =  - 3.4 \\ \text{The correct order of arrangements will be,}\\  - \dfrac{{\sqrt {80} }}{4} >  - 3\dfrac{2}{5} >  - \sqrt {20}  >  - 4\sqrt 5 $

 Which of the following is largest among all the given numbers? $ \\ \sqrt 2 ,(4 + \sqrt 5 ),(6 - \sqrt 2 ),(2 + 2\sqrt 2 )$

 Value of $\sqrt 2  = 1.414,\sqrt 5  = 2.27$. Convert all the numbers in decimal form, then by comparing the value analyse the greatest number.

 $\text{The decimal representation will be,}\\   \sqrt 2  = 1.414 \\  (4 + \sqrt 5 ) = (4 + 2.27) \approx 6.67 \\  (6 - \sqrt 2 ) = (6 - 1.414) \approx 4.586 \\  (2 + 2\sqrt 2 ) = (2 + (2 \times 1.414)) = (2 + 2.828) \approx 4.828 \\ \therefore (4 + \sqrt 5 ) = (4 + 2.27) \approx 6.67 \\ \text{Which is maximum among all the numbers.}$

 Which of the following is the proper order for organising the numbers in descending order?

 When comparing numbers, always convert the given numbers to decimal form first, then arrange the numbers in descending order.

 W.K.T $\sqrt{2}  = 1.414$ So, From the given value, if we arrange all the numbers in descending order, the value of $+2$, is the highest value. Then, the correct arrangement will be, $ \\ 2 > \sqrt 2  >  - 2 >  - 3.78$

 Which of these is the correct order of arranging all the real numbers in increasing order?

 Convert all of the given numbers to decimal form, and then compare the decimal values of the given terms.

 The decimal value of all the numbers will be, $\\   - \sqrt 7  \approx  - 2.65 \\   \Rightarrow - \sqrt 5  \approx  - 2.24 \\  \Rightarrow  - \sqrt {\dfrac{{11}}{2}}  =  - \sqrt {5.5}  \approx  - 2.35 \\  \Rightarrow  - \dfrac{{13}}{4} =  - 3.25 \\  \Rightarrow  - \dfrac{{11}}{4} =  - 2.75 \\ $ From the above obtained value arrange all the numbers on number line, $\\ -2.24 > – 2.35$ Similarly, $- 2.35 > – 2.65, \\ \therefore - \dfrac{{13}}{4} <  - \dfrac{{11}}{4} <  - \sqrt 7  <  - \sqrt {\dfrac{{11}}{2}}  <  - \sqrt 5 $<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/dfcef655-045a-4c10-9fd8-ce29d165aed15532631833574885910.png"/>