Question

$(\sqrt{2} - \sqrt{3} ) \times ( \sqrt{3} - \sqrt{2} )$
is this an irrational number?
with explaination
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Answer 1

Answer:

Step-by-step explanation:

Yes, this is an irrational number.

Given that,

( √2 - √3 ) × ( √3 - √2 )

= √2 ( √3 - √2) - √3 ( √3 - √2 )

= √6 - ( √2 )² - [ ( √3)² - √6 ) ]

= √6 - 2 - ( 3 - √6 )

= √6 - 2 - 3 + √6 ( ∵ - × + = - ; - × - = + )

= - 5 + 2√6

Answer 2

$\small\colorbox{lightyellow} {\text{ \bf♕ Brainliest answer }}$$\rule{300pt}{0.1pt}$$\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}$$\rule{300pt}{0.1pt}$

Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd.

$\rm \implies\sqrt{6}-2-3+\sqrt{6}$

Collect like terms.

$\implies(\sqrt{6}+\sqrt{6})+(-2-3)$

$\boxed{\red{ \tt\implies 2 \sqrt{6} - 5}}$