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

1 Answer
Jun 21, 2016

Answer:

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#