Question

minus 1 + root 3 whole cube is a real number show that

Answer 1

(√3 -1)³ = 3√3 -1 - 3√3(√3-1)
= 3√3 -1 - 9 + 3√3
= 6√3 -10
it's an irrational number.
so, it is a real no.

Answer 2

Answer:

$(-1+\sqrt3)^3$ is a real number.

Step-by-step explanation:

To show : $(-1+\sqrt3)^3$ is a real number ?

Solution :

We solve the expression using cubic identity,

$(a+b)^3=a^3+b^3+3a^2b+3ab^2$

$(-1+\sqrt3)^3=(-1)^3+(\sqrt3)^3+3(-1)^2(\sqrt3)+3(-1)(\sqrt3)^2$

$(-1+\sqrt3)^3=-1+3\sqrt3+3\sqrt3-9$

$(-1+\sqrt3)^3=-10+6\sqrt3$

As the solution does not contain an imaginary term.

Therefore, $(-1+\sqrt3)^3$ is a real number.