Answer:
The nature of the result of the given expression is irrational. (Option 2)
Step-by-step explanation:
Let's simplify the given expression by rationalizing the denominator. To rationalize the denominator, multiply both numerator and denominator by √2.
![(4+√(3))/(√(2))*(√(2))/(√(2))](https://img.qammunity.org/2023/formulas/mathematics/college/fn7pedy2svudo4o9iavltbplezpligt97i.png)
![=(4(√(2))+√(3)(√(2)))/(√(2)(√(2)))](https://img.qammunity.org/2023/formulas/mathematics/college/q0o5rpa7lvghkrvsv1m4mww16j88n4w9ek.png)
![=(4√(2)+√(6))/(2)](https://img.qammunity.org/2023/formulas/mathematics/college/jvhmp9jgjalsu1o3byizxjzs3c1jisnxf1.png)
The result is shown above. When converted to a decimal number, it is equivalent to 4.053171996.
As we can see, the result is neither an integer nor a whole number because these two don't have decimal points.
In addition, the result is not a rational number because the equivalent decimal number is both non-terminating and non-repeating decimal.
Hence, the result is an irrational number. (Option 2)