Solve a surd ( 5-sqrt2)²?

2 Answers
Apr 12, 2018

27-10sqrt2

Explanation:

"note that "sqrtaxxsqrta=a

(5-sqrt2)^2=(5-sqrt2)(5-sqrt2)

"expand the factors using FOIL"

rArr(5-sqrt2)(5-sqrt2)

=25-5sqrt2-5sqrt2+(sqrt2xxsqrt2)

=25-10sqrt2+2=27-10sqrt2

Apr 13, 2018

27-10sqrt2

Explanation:

(5-sqrt2)^2 = (5-sqrt2)(5-sqrt2)

Multiply each term:

5 xx 5=25

5 xx -sqrt2=-5sqrt2

-sqrt2 xx 5=-5sqrt2

-sqrt2 xx -sqrt2=sqrt4=2

Collecting like terms:

25+2+(-5sqrt2)+(-5sqrt2) -> 27-10sqrt2