How do you simplify $(4-sqrt3)(12+5sqrt3)$ ?

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Answer 1 · 2016-02-07T02:52:16

$33+8sqrt3$

Begin by expanding the brackets. By doing this we get:

$4*12+4*5sqrt3-sqrt3*12-sqrt3*5sqrt3$

Now if we do the multiplications we get:

$48 +20sqrt3-12sqrt3-15$

We can now simplify by gathering the like terms:

$33+8sqrt3$

Answer 2 · 2016-02-07T02:57:43

Multiply everything with everything.

$(4 - sqrt(3))(12 + 5sqrt(3))$

= $48 - 12sqrt(3) + 20sqrt(3) - 5sqrt(9)$

= $48 - 15 + 8sqrt(3)$

= $33 + 8sqrt(3)$

Practice exercises:

a) $(3 - 2sqrt(5))(4 + sqrt(10))$

b) $(4sqrt(6) + 5sqrt(11))(3sqrt(7) - 9)$

c) $(2 + sqrt(13))(2 - sqrt(13))$

d) $(sqrt(2) - sqrt(15))^2$

How do you simplify (4-sqrt3)(12+5sqrt3)(4-sqrt3)(12+5sqrt3)?