How do you simplify √36−4x2?

2 Answers
Jim S
Jan 11, 2018

√36−4x2=2√(3−x)(3+x)

Explanation:

√36−4x2=2√(3−x)(3+x)

because:

36−4x2=4(9−x2)=4(32−x2)=4(3−x)(3+x)=−4(x−3)(x+3)

As a result :

√36−4x2=√4(3−x)(3+x)=√4⋅√(3−x)(3+x)=2√(3−x)(3+x)

Jim G.
Jan 11, 2018

2√(3−x)(3+x)

Explanation:

factorise the radicand

36−4x2=4(9−x2)←common factor of 4

9−x2 is a difference of squares

∙xa2−b2=(a−b)(a+b)

9−x2=32−x2=(3−x)(3+x)

⇒√36−4x2

=√4(x−3)(x+3)

=2√(x−3)(x+3)

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