How do you simplify $(sqrt2 + sqrt6)(sqrt2 - sqrt6)$ ?

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Answer 1 · 2016-06-02T22:11:20

The result is -4.

When you multiply two numbers in the form $(A+B)(A-B)$ you obtain as result $A^2-B^2$ .

In your case $A=sqrt(2)$ and $B=sqrt(6)$ then

$(sqrt(2)+sqrt(6))(sqrt(2)-sqrt(6))=sqrt(2)^2-sqrt(6)^2=2-6=-4$ .

Answer 2 · 2016-06-02T22:15:34

$2 - 6 = -4$

This is in the same format as $(x + y)(x - y)$ which are the factors of $x^2 - y^2, " known as the difference between two squares"$

So if $(x + y)(x - y) = x^2 - y^2$ , then

$(sqrt2 + sqrt6)(sqrt2 - sqrt6) = (sqrt2)^2 - (sqrt6)^2$

This simplifies to $2 - 6 = -4$

This could also be simplified by multiplying out the brackets to get 4 terms, but the answer will be the same - it will just take longer.

How do you simplify (sqrt2 + sqrt6)(sqrt2 - sqrt6) (sqrt2 + sqrt6)(sqrt2 - sqrt6)?