Question

Classify given equation as rational or irrational:2 root 3 + 3 root 2 - 4 root 3 + 7 root 2

Answer 1

Irrational

Step-by-step explanation

`2√(3)+3√(2)-4√(3)+7√(2)`

Step 1

simplify

`\begin{gathered} 2√(3)+3√(2)-4√(3)+7√(2) \\ \lparen2-4)√(3)+\left(3+7\right)√(2) \\ -2√(3)+4√(2) \\ \end{gathered}`

Step 2

the square root of 2 is an irrational number,because there is not number such that

`√(2)=(a)/(b)`

and

The square root of 3 is an irrational number √3 cannot be expressed in the form of p/q

hence

the sum of 2 irrational numbers gives a irrational result,Sum of two irrational numbers is always irrational.

so, the answer is

Irrational

I hope this helps you