Question

state whether the number
$( { \sqrt{2 - \sqrt{3} } )( \sqrt{2 + \sqrt{3} )$
is the rational or irrational justify

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Answer 1

The given number is rational, because ;

(√2 - √3)(√2 + √3) = (√2)² - (√3)² = 2 - 3 = -1, which is an integer and, every integer is a rational number.

Hope it'll help you.....

Answer 2

HEY MATE HERE IS YOUR ANSWER.

= ( 2 - √3 ) ( 2 + √3 )

= ( 2 ² - √3 ² ) { ( a + b )(a - b ) = a ² - b ²}

= 4 - 3

= 1

1 IS AN INTEGER. THEREFORE IT IS A RATIONAL NUMBER.