i was wondering how do you solve radical equations like multiplication , addition and or subtraction?when you answer could you please provide an example with the explenation please

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should know that radiacl equations are also called irrational equations. The method you use when you need to solve this kind of equation aims the removal of radical sign.

Hence, if you want to solve the irrational equation sqrtx + sqrt(x-4) = 2, you need to isolate one radical to one side, moving the other radical to the right side such that:

sqrt x = 2 - sqrt(x-4)

You need to remove the square root, hence you need to raise to square the radical from the left side, but you also need to perform the squaring operation to the right side, to preserve the equilibrium such that:

(sqrt x) = (2 - sqrt(x-4))^2

Notice that if there is more then one term, you need to raise to square all the right side.

x = 4 - 4sqrt(x-4) + x - 4

Notice that sqrt(x-4) may stay at its place, as well.

You need to reduce like terms such that:

0 = - 4sqrt(x-4)

You need to divide by -4 both sides such that:


Raising to square both sides yields: x - 4 = 0


You need to check if x=4 works as solution to equation such that:

sqrt 4 + sqrt(4-4) = 2 => 2 + 0 = 2 => 2 = 2

Hence, the solution to the equation is x=4.

Notice that if the order of root is larger than 2, you need to raise to a power equal to order of the root.