Is 5^2 +4 ^2 the sum of two like radicals? What else could be made or produce from this problem?

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`5^2+4^2=25+16=41`

If you meant `sqrt(5)+sqrt(4)=sqrt(5)+2` -- the radicals would not be like radicals. Like radicals have the same expression in the radicand e.g. `3sqrt(2)+4sqrt(2)=7sqrt(2);3sqrt(5xy)+4sqrt(5xy)=7sqrt(5xy)`

Adding/subtracting like radicals is really just the distributive property:

`3sqrt(5xy)+4sqrt(5xy)=sqrt(5xy)(3+4)=7sqrt(5xy)`

In the most case : `sqrt(x)+sqrt(y) != sqrt (x+y)`

Indeed if: `sqrt(x)+sqrt(y)=sqrt(x+y)` then squaring:

`x+y+2sqrt(xy)=x+y`

That is: `sqrt(xy)=0`

It means it hold true in trivial solutionif, only if `x=0` or `y=0`

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