Question

what is the smaller number by what root 5 - root 2 is to be multipled to a rational number also find the number so obtained

Answer 1

Logically thinking , it should be ‘0’ (smallest non-negative no. to make the product a rational no. , i.e. 0 itself)

But for smallest (+ve) no. , (√5 - √2) should be multiplied with its conjugate , i.e. (√5 + √2) to get a rational no.

The resultant Rational no. will be :

(√5 - √2)(√5 + √2) = (√5)^2 - (√2)^2    (a-b)(a+b) = a^2 – b^2
                                 = 5 -2
                                 = 3

Hope that it was helpful .   :)