The full question is: "How can we take square root of both sides of an inequality or equation just by multiplying each side by numbers with negative rational exponents". I will include several examples to explain how I think about it.(adsbygoogle = window.adsbygoogle || []).push({});

1)a=b, a^(-0.5)*a=b*a^(-0.5) (but a^(-0.5)=b^(-0.5)) then a^(-0.5)*a=b*b^(-0.5) which is sqrt(a)=sqrt(b)

2)a>0 b>0

a>b

a^(-0.5)*a>b*a^(-0.5) b^(-0.5)*a>b^0.5 ???

a^(0.5)=b*a^(-0.5)??? (Trying to prove that sqrt(a)>sqrt(b))

3)x^2=2.5

x^(-1)*x^2=2.5*2.5^(-0.5) (2.5^(-0.5)=x^(-1))

x=sqrt(2.5)

Which is incorrect. Because the true solution is sqrt(x^2)=sqrt(2.5) then |x|=sqrt(2.5) and x1=+sqrt(2.5), x2=-sqrt(2.5)

(The question has similarities with this one https://www.physicsforums.com/threa...-equation-and-inequality.823960/#post-5174108)

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# Alternative path to taking roots of both sides of equation

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