If $$a = 28 - 5\sqrt{12}$$ and $$b = 2 + \sqrt{3}$$​, find the value of $$(a\sqrt{3} + b)$$​​

Correct option is D

Given:

a = $$28 - 5\sqrt{12}​$$​​

b = $$2 + \sqrt{3}​$$​​

Solution:

Simplify a:

​$$a = 28 - 5\sqrt{12} = 28 - 5 \times 2\sqrt{3} = 28 - 10\sqrt{3}$$​​

Now, calculate $$a\sqrt{3}​:$$​​

​$$a\sqrt{3} = (28 - 10\sqrt{3})\sqrt{3} = 28\sqrt{3} - 10 \times 3 = 28\sqrt{3} – 30$$​​

Simplify b:

​$$b = 2 + \sqrt{3}$$​​

Now, compute $$a\sqrt{3} + b:$$​​

​$$a\sqrt{3} + b = (28\sqrt{3} - 30) + (2 + \sqrt{3}) = 28\sqrt{3} - 30 + 2 + \sqrt{3}$$​​

​$$a\sqrt{3} + b = 28\sqrt{3} + \sqrt{3} - 30 + 2 = 29\sqrt{3} - 28$$​​