Question

Which of the irrational number does not lie between $\frac{3}{25}$ and $\frac{7}{25}$ ?

• A. $-\sqrt{2}$
• B. $\sqrt{7}$
• C. $4-\sqrt{2}$
• D. $2-\sqrt{3}$

Answer 1

Answer: (A), (B), (C)

$4-\sqrt{2}$

On converting fraction into decimal we get,
$\frac{3}{25}=0.12$ and $\frac{7}{25}=0.28$.

$\underset{–}{\text{Option (a)}}$ Since these numbers are positive so no negetive number will lie between them, $-\sqrt{2}$ will not lie between them.

$\underset{–}{\text{Option (b)}}$ approximate value of
$2.6<\sqrt{7}<2.7$
Hence, it also does not lie between $0.12$ and $0.28$

$\underset{–}{\text{Option (c)}}$
$1.4<\sqrt{2}<1.5\Rightarrow -1.4>-\sqrt{2}>-1.5\Rightarrow 4-1.4>4-\sqrt{2}>4-1.5\Rightarrow 2.6>4-\sqrt{2}>2.5$
Hence, $4-\sqrt{2}$ does not lie between given rational numbers.

$\underset{–}{\text{Option (d)}}$
$1.73<\sqrt{3}<1.74\Rightarrow -1.73>-\sqrt{3}>-1.74\Rightarrow 2-1.73>2-\sqrt{3}>2-1.74\Rightarrow 0.27>2-\sqrt{3}>0.26$
Hence, $2-\sqrt{3}$ lie between given rational numbers.