Question

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

Answer 1

5

Explanation:

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

`(sqrt5)^2=5`

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`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`