Question

Examine, whether the following numbers are rational or irrational:
i) (2 – √2)(2 + √2)
ii) (√3 + √2)^2
iii root 24/8+root 54/9

Answer 1

Answer:

i.. ) by the algebraic identities (a+b ) (a-b) = a^2-b^2 = 2^2-√2^2 = 4-2 = 2 is rational number

ii...) by the algebraic identities (a+b)^2 = a^2 +2ab +b^2 = √3^2+√2^2+2*√3*√2= 3+2+2√6= 5+2√6 is an irrational number .

iii ...) solution is equal to the 2√6/2√2 + 8+3√6/3

= √3+8+√6 = √3(1+√2) +8 is an irrational number ...

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