Show that (4+√12)(5-√3)= 14+6√3

First, expand out the brackets. Initially, this will give you 20 - 4√3 + 5√12 - √36.

√36 is the equivalent of 6, now giving up 20 - 4√3 + 5√12 - 6. We can combine the 20 and the 6 to give us 14 - 4√3 + 5√12.

Now, let's look at 5√12. √12 is the same as √4 x √3. √4 is the same as 2, so we have 2√3. We then substitute in 2√3 as √12, giving us 5(2√3). This then becomes 10√3.

We then have 14 - 4√3 + 10√3. We can then do 10√3 - 4√3, which gives us 6√3.

Altogether, this gives us our answer of 14 + 6√3!