How do you simplify #\sqrt{36-4x^{2}}#?

2 Answers
Jim S
Jan 11, 2018

#sqrt(36-4x^2)=2sqrt((3-x)(3+x))#

Explanation:

#sqrt(36-4x^2)=2sqrt((3-x)(3+x))#

because:

#36-4x^2=4(9-x^2)=4(3^2-x^2)=4(3-x)(3+x)=-4(x-3)(x+3)#

As a result :

#sqrt(36-4x^2)=sqrt(4(3-x)(3+x))=sqrt4*sqrt((3-x)(3+x))=2sqrt((3-x)(3+x))#

Jim G.
Jan 11, 2018

#2sqrt((3-x)(3+x))#

Explanation:

#"factorise the radicand"#

#36-4x^2=4(9-x^2)larrcolor(blue)"common factor of 4"#

#9-x^2" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#9-x^2=3^2-x^2=(3-x)(3+x)#

#rArrsqrt(36-4x^2)#

#=sqrt(4(x-3)(x+3))#

#=2sqrt((x-3)(x+3))#

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