Question

An expression is given: 2(Vk-1) +V8 If on adding -8v2 to the expression results in a rational number, what is the value of k?

Answer 1

•ALGEBRIC EXPRESSIONS:-

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently, by clearing denominators, with integer coefficients).

The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.

All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as π and e, are called transcendental numbers.

The set of complex numbers is uncountable, but the set of algebraic numbers is countable and has measure zero in the Lebesgue measure as a subset of the complex numbers. In that sense, almost all complex numbers are transcendental.