Question

Examine whether the following numbers rational and irrational (i) (3+√2) ² (ii) (2+√2) (2-√2) (iii) 6/√3

Answer 1

Answer:

(i) (3+√2)² = 3² + 2(√2)(3) + (√2)²

. = 9 + 6√2 + 2

. = 11 + 6√2

It's not a rational number

(ii) (2+√2) (2-√2) = 2² - (√2)² [Using Identity (a+b)(a-b) = a² - b²]

= 4 - 2 = 2

It's a rational number

(iii)

$\frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{6 \sqrt{3} }{ {( \sqrt{3}) }^{2} } = \frac{6 \sqrt{3} }{3} = 2 \sqrt{3}$

it's not a rational number