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)

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestRemember that \(\sqrt{x^{2}} \not = x \Rightarrow \sqrt{x^{2}} = |x|\)

Log in to reply

The contradiction you get is precisely why mathematicians decided to say \( \sqrt{x^{2}} = |x|\)

Log in to reply

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 \(b = -1 \rightarrow \sqrt{5}= \sqrt{5*(-1)^{2}} = -(-1)\sqrt{5} = \sqrt{5}\)

Log in to reply

Log in to reply