The rational number betwen the pair of numbers 1/2 and √1 isA) 9/4B)

1.	The rational number betwen the pair of numbers 1/2 and √1 isA) 9/4B) 3/4C) 5/4D) 7/4
Answer» Correct option is (B) 3/4 Rational number which lies between \(\frac{1}{2}\) and \(\sqrt1\) \(=\frac{\frac12+\sqrt1}2\) \(=\frac{\frac12+1}2\) \(=\frac{\frac32}2\) \(=\frac3{2\times2}\) \(=\frac34\) Alternative :- \(\because\) \(\frac{1}{2}\) = 0.5 and \(\sqrt1\) = 1 Now, (A) \(\frac{9}{4}=2+\frac14\) = 2.25 > 1 (B) \(\frac{3}{4}\) = 0.75 which lies between 0.5 and 1. \(\therefore\) \(\frac{1}{2}\) < \(\frac{3}{4}\) < \(\sqrt1\) (C) \(\frac{5}{4}\) = 1 + \(\frac14\) = 1.25 > 1 (D) \(\frac{7}{4}\) = 1 + \(\frac{3}{4}\) = 1.75 > 1 Correct option is B) 3/4

The rational number betwen the pair of numbers 1/2 and √1 isA) 9/4B) 3/4C) 5/4D) 7/4

Answer»

Correct option is (B) 3/4

Rational number which lies between \(\frac{1}{2}\) and \(\sqrt1\)

\(=\frac{\frac12+\sqrt1}2\) \(=\frac{\frac12+1}2\) \(=\frac{\frac32}2\)

\(=\frac3{2\times2}\) \(=\frac34\)

Alternative :-

\(\because\) \(\frac{1}{2}\) = 0.5 and \(\sqrt1\) = 1

Now, (A) \(\frac{9}{4}=2+\frac14\) = 2.25 > 1

(B) \(\frac{3}{4}\) = 0.75 which lies between 0.5 and 1.

\(\therefore\) \(\frac{1}{2}\) < \(\frac{3}{4}\) < \(\sqrt1\)

(D) \(\frac{7}{4}\) = 1 + \(\frac{3}{4}\) = 1.75 > 1

Correct option is B) 3/4