Solve a surd ( 5-sqrt2)²?

2 Answers
Apr 12, 2018

27-10sqrt227102

Explanation:

"note that "sqrtaxxsqrta=anote that a×a=a

(5-sqrt2)^2=(5-sqrt2)(5-sqrt2)(52)2=(52)(52)

"expand the factors using FOIL"expand the factors using FOIL

rArr(5-sqrt2)(5-sqrt2)(52)(52)

=25-5sqrt2-5sqrt2+(sqrt2xxsqrt2)=255252+(2×2)

=25-10sqrt2+2=27-10sqrt2=25102+2=27102

Apr 13, 2018

27-10sqrt227102

Explanation:

(5-sqrt2)^2 = (5-sqrt2)(5-sqrt2)(52)2=(52)(52)

Multiply each term:

5 xx 5=255×5=25

5 xx -sqrt2=-5sqrt25×2=52

-sqrt2 xx 5=-5sqrt22×5=52

-sqrt2 xx -sqrt2=sqrt4=22×2=4=2

Collecting like terms:

25+2+(-5sqrt2)+(-5sqrt2) -> 27-10sqrt225+2+(52)+(52)27102