Question

Which of the following is not irrational (a) (2-√3)2 (b) (√2+√3)2 (c) (√2-√3) (√2+√3) (d) 2√7/7

Answer 1

Answer:

c .  $(\sqrt{2} -\sqrt{3} ) (\sqrt{2} + \sqrt{3} )$

Step-by-step explanation:

Option C is not irrational

because,

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

= $\sqrt{2} ^{2} - \sqrt{3} ^{2}$     $using identity: (a - b) (a + b) = a^{2} -b^{2}$

= 2 - 3

= -1 ( this is rational number)

Answer 2

Given:

(a) (2-√3)2

(b) (√2+√3)2

(c) (√2-√3) (√2+√3)

(d) $\frac{2\sqrt{7} }{7}$

To find:

The non irrational number.

Solution:

Irrational numbers are the real numbers that cannot be expressed as a simple fraction.

The decimal expansion of an irrational number is neither terminating nor recurring.

(a) (2-√3)2

On simplifying we get,

4 - 2√3 which is a irrational number.

(b) (√2+√3)2

On simplifying we get,

2√2 + 2√3 , which is a irrational number.

(c) (√2-√3) (√2+√3)

On simplifying we get,

(√2)² - (√3)² = 2 - 3

(√2-√3) (√2+√3)  = -1 , which is not irrational number.

d) $\frac{2\sqrt{7} }{7}$

On simplifying we get,

$\frac{2}{\sqrt{7} }$  , which is a irrational number.

Final answer:

The non irrational number among the given numbers is (c) (√2-√3) (√2+√3)