How would you simplify (sqrt13 - sqrt3) ( sqrt13 + sqrt 3)(√13−√3)(√13+√3)?

1 Answer
Meave60
Feb 24, 2016

(sqrt 13-sqrt3)(sqrt 13+sqrt 3)=10(√13−√3)(√13+√3)=10.

Explanation:

(sqrt 13-sqrt3)(sqrt 13+sqrt 3)(√13−√3)(√13+√3)

This is an example of the difference of squares, a^2-b^2=(a+b)(a-b)a2−b2=(a+b)(a−b), where a=sqrt13a=√13 and b=sqrt 3b=√3.

Rewrite the expression as a difference of squares.

sqrt13^2-sqrt3^2√132−√32

Apply the square root rule sqrta^2=a√a2=a.

13-313−3

Simplify.

1010

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