Solve a surd ( 5-sqrt2)²?

2 Answers
Jim G.
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#

Brandon
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#

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