Question

(5√3-√27)^3
how do you prove that this is an integer?

Answer 1

It is not an integer.

Explanation:

`(5√(3) -√(27) )^3\\\\=(√(3) *(5-3))^3\\\\=8*3*√(3) \\\\=24√(3) \\`

Answer 2

Keys:

• 
  `\left(a\cdot \:b\right)^n=a^nb^n`

Explanation:

`\left(5√(3)-√(27)\right)^3\\\5√(3)-√(27)^3=\left(2√(3)\right)^3\\= 2√(3)\\\left(2√(3)\right)^3=2^3\left(√(3)\right)^3\\=2^3\left(√(3)\right)^3\\2^3=8\\=8\left(√(3)\right)^3\\=8\cdot \:3√(3)\\8\cdot \:3=24\\=24√(3)`