Question

Identify the irrational number among the following numbers.
(i) (1+√3)-(√3-1),
(ii) 2+5√5-√125,
(iii) π/2π,
(iv) √2/2+√2/2​

Answer 1

(i)

$(1 + \sqrt{3} ) - ( \sqrt{3} - 1) \\ = 1 + \sqrt{3} - \sqrt{3} + 1 \\ = 1 + 1 \\ = 2$

(ii)

$2 + 5 \sqrt{5} - \sqrt{125} \\ = 2 + 5 \sqrt{5} - (\sqrt{25} \times \sqrt{5} ) \\ = 2 + 5 \sqrt{5} - 5 \sqrt{5} \\ = 2$

(iii)

$\frac{\pi}{2\pi} \\ = \frac{\pi}{\pi} \times \frac{1}{2} \\ = \frac{1}{2}$

(iv)

$\frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} \\ = \frac{ \sqrt{2} + \sqrt{2} }{2} \\ = \frac{2 \sqrt{2} }{2} \\ = \sqrt{2}$

Hope this helps. Thanks.