multiply square roots

Question

(√2+√3)(√2-√3)

Answer 1

(√2+√3)(√2-√3)

This product is equal to the difference of the squares =

(2-3) = -1

Answer 2

This problem can be approached using the FOIL method where you multiply the first terms in each parentheses, then the outer terms, then the inner terms, and finally the last terms.

 

So, from the problem above, 

(√2+√3)(√2-√3)= √(2) *√(2)+√(2)*-√(3)+√(3)*√(2)+√(3)*-√(3)

 

From here we see that the first term reduces to 2 since  √(2) *√(2)=2.

The next two terms, √(2)*-√(3) and √(3)*√(2), cancel out since the first term equals -√6 and the second term equals √6, when they are added together they equal zero. The last term √(3)*-√(3) equals -3 since when √(3) is multiplied by itself the product is 3 and one of the square roots has a negative sign.

 

Therefore, the final answer is 2+0-3=2-3=-1.

 

Remember when you are using the foil method, you have to include all necessary signs in your calculations.