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Simplifying Radical Expressions

. . .

Applying All the Rules



Math - Simplifying Radicals

Simplifying Radical Expressions - . . .

Combining all the rules: addition, multiplication, division,
rationalizing the denominator, fractional & decimal exponents, etc. . . .


Introduction to Simplifying Aggregate Expressions containing Exponents & Roots:


Simplifying an expression means to reduce the complexity of the expression without changing its value .


There are 3 reasons to simplify expressions containing exponents

and radicals:
  • Simplifying an expression usually makes it smaller and less cumbersome than the original. Simplifying expressions containing exponents and roots is similar to simplifying fractions by reducing them as much as possible. In both cases, it makes them easier to understand.
  • Simplifying expressions is an important intermediate step when solving equations.
  • Simplifying expressions makes those expressions easier to compare with other expressions (which have also been simplified).

The simplification process brings together all the rules and properties which apply to real numbers. This includes simplifying exponents, parentheses, fractions, multiplied results, rationalizing the denominator, and combining like terms - as well as using all the properties of numbers: associative, distributive, commutative, etc.

See examples below.

Examples of How to Simplify Radical Expressions

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Math - Simplifying Radical Expressions - example 1 Simplify the following expression: Math - Simplifying Radical Expressions - Initial Problem - example 1


Math - Simplifying Radical Expressions - example 1

The final answer is: Math - Simplifying Radical Expressions - Final Answer - example 1




Math - Simplifying Radical Expressions - example 2 Simplify the following expression: Math - Simplifying Radical Expressions - Initial Problem - example 2


Math - Simplifying Radical Expressions - example 2

The final answer is: Math - Simplifying Radical Expressions - Final Answer - example 2




Math - Simplifying Radical Expressions - example 3 Simplify the following expression: Math - Simplifying Radical Expressions - Initial Problem - example 3


Math - Simplifying Radical Expressions - example 3

The final answer is: Math - Simplifying Radical Expressions - Final Answer - example 3




Math - Simplifying Radical Expressions - example 2 Simplify the following expression: Math - Simplifying Radical Expressions - Initial Problem - example 4


Math - Simplifying Radical Expressions - example 4

The final answer is: Math - Simplifying Radical Expressions - Final Answer - example 4