How do you multiply $sqrt[5] * sqrt[5]$ ?

Question

14404 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-21T19:49:29

5

Writing this another way we have $(sqrt5)^2$

$(sqrt5)^2=5$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(brown)("How squaring a square root works")$

$color(blue)("Point 1")$
Squaring the square root has almost the same effect of not having taken the square root in the first place.

$color(blue)("Point 2")$
Suppose we write the square root of 5 as $x$ .

Then $(-x)xx(-x) = +5$
and $(+x)xx(+x)=+5$

So $sqrt(5)$ has 2 answers. These are a positive value and also a the same number but it is negative. ( $+x" or "-x$ ).

$color(blue)("Point 3")$
As the whole thing is squared then it does not matter if we look at $-x$ or $+x$ as the answer is always going to be +5

as $(-x)xx(-x)=+5" and "(+x)xx(+x)=+5$

How do you multiply sqrt[5] * sqrt[5]sqrt[5] * sqrt[5]?