Question

Is product (√3-1)(2+√3) is an irrational numbers? state whether it is true or false justify your answer ​

Answer 1

(√3−1)(2+√3)

=1+√3(Decimal: 2.732051)

Answer 2

Given :  product (√3-1)(2+√3) is an irrational number

To Find :  true or false

Solution:

(√3-1)(2+√3)

=√3 (2+√3)  -  1(2+√3)

= 2√3 + 3 -  2 -  √3

=  1  + √3

is an irrational number    (∵ sum of a rational number and an irrational number is always an irrational number  and 1 is rational and √3 is irrational )

Hence product (√3-1)(2+√3) is an irrational number is TRUE

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