Question

show that (2+√5)(2-√5)(3+√2)(3-√2) is a rational number

Answer 1

Answer:

(2 + √5)(2-√5)(3+√2)(3-√2)

= (2² - √5²)(3² - √2²)

= ( 4 - 5)( 3 -2)

= -1 × 1

= -1

that is rational number.

Step-by-step explanation:

formula used

( a+ b)(a - b) = a² - b²

Answer 2

$\implies(2 + \sqrt{5})(2 - \sqrt{5})(3 + \sqrt{2})(3 - \sqrt{2}) \\ \\ \\ \implies( {2}^{2} - { \sqrt{5} }^{2})( {3}^{2} - { \sqrt{2} }^{2}) \\ \\ \\ \implies(4 - 5)(9 - 2) \\ \\ \\ \implies - 1 \times 7 \\ \\ \\ \implies - 7$

so -7 is a rational number