An equation that contains roots involving variables, such as √(x-5) =2 is called a radical equation. The main goal in solving them is to get rid of roots and to convert the radical equation to some simple, known equation.
Product rule for radicals:
n√a . n√b = n√ab
Quotient rule for radicals:
n√a / n√b = n√a/b
Adding and Subtracting Radical Expressions:
We can add or subtract radicals using the distributive property.
Example: 5√3 +2√3
Multiplying Radical Expressions:
Using special product rule with radicals:
(a-b) .(a+b) = a2 +b2
x= √(3x+7) -1
Adding 1on both side x+1 = √(3x+7)
Squaring both side x2+2x+1=3x+7
Subtracting 3x+7 from both side:
x2 + x-6=0
So x = -2 and x = 3, but only x =3 makes the original equation equal.
Dividing by a complex number: