Waste less time on Facebook — follow Brilliant.
×

I think I broke math

So I've been pondering this question for a while now and I cant see anything wrong. Please tell me where I go wrong in the following equations:

If...

\(\sqrt{ab^2}=b\sqrt{a}\)

Then

\(\sqrt{5}=\sqrt{5(-1)^2}=(-1)\sqrt5\)

Therefore

\(\sqrt5=-\sqrt5\)

How is this possible. (There has to be some simple detail I missed)

Note by Trevor Arashiro
2 years, 8 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Remember that \(\sqrt{x^{2}} \not = x \Rightarrow \sqrt{x^{2}} = |x|\) Jordi Bosch · 2 years, 8 months ago

Log in to reply

@Jordi Bosch The contradiction you get is precisely why mathematicians decided to say \( \sqrt{x^{2}} = |x|\) Jordi Bosch · 2 years, 8 months ago

Log in to reply

@Jordi Bosch I'll work with this case if necessary \( \sqrt{ab^{2}} = b\sqrt{a}\) if b > 0 and \( \sqrt{ab^{2}} = -b\sqrt{a}\) if b < 0. Since in this case \(b = -1 \rightarrow \sqrt{5}= \sqrt{5*(-1)^{2}} = -(-1)\sqrt{5} = \sqrt{5}\) Jordi Bosch · 2 years, 8 months ago

Log in to reply

@Jordi Bosch .Ahh, that makes sense. Thanks for the explanation Trevor Arashiro · 2 years, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...