Question

What is the nature of the result of the expression ?

Answer 1

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))`
`=(4(√(2))+√(3)(√(2)))/(√(2)(√(2)))`
`=(4√(2)+√(6))/(2)`

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)