Question

What is the nature of the result of the expression ?

Answer 1

Answer:

The nature of the result of the given expression is irrational. (Option 2)

Explanation:

Let's simplify the given expression by rationalizing the denominator. To rationalize the denominator, multiply both numerator and denominator by √2.

$\frac{4+\sqrt{3}}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}$$=\frac{4(\sqrt{2)}+\sqrt{3}(\sqrt{2})}{\sqrt{2}(\sqrt{2})}$$=\frac{4\sqrt{2}+\sqrt{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)