Question

Please help???

Why are radicals simplified before adding and
subtracting? Explain your reasoning by adding sqrt27 and
sqrt3

Answer 1

radicals are simplified because they take precedence. They take precedence just like exponents, which radicals can be written as exponents. For example

`\sqrt[3]{27} = 27^{(1)/(3)}`

Also, to add and subtract them you need to have both terms the same so that is another reason why we simplify first. If you did not simplify, the answer would not be the same and come out wrong. For instance

`√(27) = 3√(3)`

`3√(3) + √(3) = 4√(3)`
Now if you try and add without like terms(radicals) the answer would be incorrect.