Solving Radical Equations

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The meaning for the word radical is root. Radical equations is an equations which can contain constants, variables and radical included in them. Radicals can be simplified and solved. There are different mathematical operations that can be used to simplify and solve questions related to radicals. Two radicals can be added or subtracted if they have the same number or expression in the root, this makes them similar radicals to carry mathematical operations.
 
Example 1: Simplify and find the answer for the given equation
10√2x + 5√2x – 9√2x?

Solution: The given question is on adding and subtracting radicals.

This question contains the adding and subtracting the similar radical terms containing √2 with variable x.

The first step of the question is solving for 10 √2x + 5 √2x = 15 √2x

Now subtract 9 √2x from the earlier answer 15 √2x.

This makes 15 √2x – 9 √2x = 6 √2x

Therefore simplifying the radicals gives 10 √2 x + 5 √2x – 9 √2x = 6 √2x

Hence solution = 6√2x.
 
Example 2: Simplify find the answer for the given question
12 √5x + 10 √5x – 3√5x?

Solution: The given question is on adding and subtracting radicals.

This question contains the adding and subtracting the similar radical terms containing √5 with variable x.

The first step of the question is solving for 12 √5x + 10 √5x = 22 √5x

Now subtract 3√5x from the earlier answer 22√5x

This makes 22√5x – 3√5x = 19√5x.

Therefore simplifying the radicals gives 12√5x + 10√5x – 3√5x = 19√5x.

Hence solution = 19√5x.

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