Question

I don’t know how to solve this can someone please help me this is number system

Answer 1

`4√(6)-3√(3)`

Explanation:

Given rational expression:

`(2√(216)-3√(27))/(3)`

Begin by rewriting 216 as the product of 36 and 6, and 27 as the product of 9 and 3:

`(2√(36\cdot 6)-3√(9\cdot 3))/(3)`

Express 36 as 6², and express 9 as 3²:

`(2√(6^2\cdot 6)-3√(3^2\cdot 3))/(3)`

`\textsf{Apply the radical rule:} \quad √(ab)=\sqrt{\vphantom{b}a}√(b)`

`(2√(6^2)√(6)-3√(3^2)√(3))/(3)`

`\textsf{Apply the radical rule:} \quad √(a^2)=a, \quad a \geq 0`

`(2\cdot 6√(6)-3\cdot 3√(3))/(3)`

Multiply the integers in the numerator:

`(12√(6)-9√(3))/(3)`

`\textsf{Apply the fraction rule} \quad (a-b)/(c)= (a)/(c)-(b)/(c):`

`(12√(6))/(3)-(9√(3))/(3)`

Divide the integers:

`4√(6)-3√(3)`

Therefore:

`(2√(216)-3√(27))/(3)=\boxed{4√(6)-3√(3)}`