Express in surd form (2+√3)(4-√12)
you got this far OK: 8 - 2√12 + 4√3 - 6
but then you botched it
8 - 2√12 + 4√3 - 6
= 8 - 2*2√3 + 4√3 - 6
= 2
You are correct, I made an error in simplifying the expression.
8 - 2√12 + 4√3 - 6
= 8 - 2√(4*3) + 4√3 - 6
= 8 - 4√3 + 4√3 - 6
= 2
Therefore, (2+√3)(4-√12) equals 2. Thank you for pointing out the mistake.
First, we simplify the expression by expanding the brackets:
(2+√3)(4-√12)
= 2(4) + 2(-√12) + √3(4) + √3(-√12)
= 8 - 2√12 + 4√3 - √36
= 8 - 2√12 + 4√3 - 6
Next, simplify further by simplifying the surds:
= 2 - 2√3 + 4√3 - 6
= -4 + 2√3
So, (2+√3)(4-√12) = -4 + 2√3