How to Simplify Radicals

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How to Simplify Radicals
Students can learn How to simplifying radicals from the expert Math tutors available online. Students need
to understand the concept of Radicals before learning to simplify redicals. Students can get help with Math
problems involving simplify radicals from the online tutors.
The Radical is defined as the square root of a number. A radical is used to refer the irrational number. This
radical expression has been denoted in the root symbol "? ". Thus the process to Simplify Radicals involves
expressing the numbers in a simpler form or a reduced form. Students can learn to simplify radicals by the
solved examples.
Simplifying radicals include the How to simplifying radicals denominator before performing basic
mathematical operation. And given radical should satisfy the conditions and one should remember for positive
value of a the value of 1/an will always be taken as positive. Learn how to simplify radicals in this page and
learn to simplify radicals.
Examples-
Ex 1: Find the principal cube root of 125.
Solution:
125 = 5.
Therefore, the cube root of 125 is 5.
Ex2: Find the Square root of 36.
Solution: 6*6= 36
Therefore, the square root of 36 is 6.
Simplify radicals with variables
Simplify radicals with variables ,The radicals with variables should be solved n a particular order first of all we

should consider the root and then we should conside r the radicand (i.e. the part inside the root). Solve the
variables inside the root and then solve the factors using the respective root. Such that the radicals with
variables should are now in simplest form.

Examples:
Symplify [sqrt(144*x^2)]
Solution:
[sqrt(144) = 12]
[sqrt(x^2) =x]
Therefore
[sqrt( 144 * x^2) =12 * x =12x]
Simplifying radicals with fractions
How to simplify radicals with How to simplifying radicals fractions can be solved by determining the root
of the numerator and denominator separately. Simplify radicals with fractions is made much easier when we
solve them separately i.e. the numerator and denominator separately.
Example:
[sqrt(6)/6] Simplify
Solution:
[sqrt(6)/6 = sqrt(6)/(sqrt(6)*sqrt(6))]
[= 1/sqrt(6)]
Example:
Simplify [sqrt(8) /sqrt(32)]
Solution:
[sqrt(8)/ sqrt(32) = (2sqrt(2))/(4sqrt(2))]
[= 2/4]
[=1/2]
Simplifying radicals - Multiplication
When multiplying radicals, How to simplifying radicals powers can be brought under a single radical
sign, the terms inside can be
multiplied and simplified.
Example :
Simplify ?3.?8
Solution:
?3.?8 = ?24 = ?4?6 = 2?6
The FOIL method can also be used in multiplication of radical expressions.
Example :


Evaluate (5 + 2?8)(3 - 4?8)
Solution;



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