Why is it that [itex]\sqrt{a+b+2\sqrt{ab}} = \sqrt{a}+\sqrt{b}\,?[/itex]songoku said:
SammyS said:
ehild said:SammyS, you are the greatest square-root simplifier!
ehild
A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 x 5 = 25.
To simplify a square root, you need to find the largest perfect square that is a factor of the number inside the square root sign. Then, you can take the square root of that perfect square and move it outside the square root sign. The remaining number inside the square root sign is the simplified form.
No, not all square roots can be simplified. There are some numbers that do not have a perfect square as a factor, so they cannot be simplified further.
Simplifying a square root means rewriting it in its simplest form, while evaluating a square root means finding the numerical value of the square root. For example, simplifying the square root of 12 would give you √4 x √3, while evaluating it would give you the approximate value of 3.4641.
Simplifying square roots makes it easier to work with them in mathematical equations and to find approximate values without using a calculator. It can also help in finding patterns and relationships between numbers.