Question

# Which of the following irrational numbers lie between 511 and 711

A
22
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B
33
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C
51710
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D
None of the above.
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Solution

## The correct option is C √5−1710On converting given fractions in to decimals, we get: 511=0.454545... & 711=0.636363... Option(a)––––––––––– 2√2 1.4<√2<1.5⇒1.4×2<2√2<2×1.5⇒2.8<2√2<3 Hence, it does not lie between 511 & 711 Option(b)––––––––––– √33 1.7<√3<1.8⇒1.7÷3<√33<1.8÷3⇒0.5¯6<√33<0.6 Hence, it lies between 511 & 711 Option(C)–––––––––––– √5−1710 2.2<√5<2.3⇒2.2−1.7<√5−1.7<2.3−1.7⇒0.5<√5−1.7<0.6 Hence, it lies between 511 & 711 other options lie outside the given rational numbers

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