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subject: Radical Rationalized Form [print this page]

Simplifying radicals activity involves the process of solving radicals equation with step by step solution. Activity is the process of solving equations with radicals symbol. The square root symbol is also represented as radicals. Simplifying radicals is easily carried out by performing squaring operations on the given equation is known as simplifying radicals activity. The following are the example problems which explain the radicals activity.

The radical may have a square root at the denominator. To eliminate such radical in the denominator the rationalized method is used. If an expression has a single value under a square root then to rationalize the term it needs to multiply and divide the given radical form by the same number. If in the denominator it has more than one term then we have to take conjugate to rationalize the radical.

Example Problems Radical Rationalized Form:

Example 1- Radical rationalized form:

Simplify the term 'sqrt(3/2)'

Solution:

Given, 'sqrt(3/2)'

The given term can be written as '(sqrt(3))/(sqrt(2))'

In the above term it has square root in the denominator. So to simplify we have to multiply and divide the term by 'sqrt(2)' .

'(sqrt(3))/(sqrt(2))' 'xx' '(sqrt(2))/(sqrt(2))'

'(sqrt(3)*sqrt(2))/(sqrt(2)*sqrt(2))'

'(sqrt(3*2))/(sqrt(2*2))'

'(sqrt(6))/(2)'

Example 2- Radical rationalized form:

Simplify the term 'sqrt(5/3)'

Solution:

Given, 'sqrt(5/3)'

The given term can be written as '(sqrt(5))/(sqrt(3))'

In the above term it has square root in the denominator. So to simplify we have to multiply and divide the term by 'sqrt(3)' .

'(sqrt(5)*sqrt(3))/(sqrt(3)*sqrt(3))'

'(sqrt(5*3))/(sqrt(3*3))'

'(sqrt(15))/(3)'

More Example Problems Radical Rationalized Form:

Example 3 - Radical rationalized form:

Simplify the term 'sqrt(9/7)'

Solution:

Given, 'sqrt(9/7)'

The given term can be written as '(sqrt(9))/(sqrt(7))'

In the above term it has square root in the denominator. So to simplify we have to multiply and divide the term by 'sqrt(7)'

'(sqrt(9))/(sqrt(7))' 'xx' '(sqrt(7))/(sqrt(7))'

'(sqrt(9)*sqrt(7))/(sqrt(7)*sqrt(7))'

'(3*sqrt(7))/(sqrt(7*7))'

'(3sqrt(7))/(7)'

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Example 4 - Radical rationalized form:

Simplify the term'(sqrt(2)+3)/(sqrt(2)+5)' .

Solution:

Given, '(sqrt(2)+3)/(sqrt(2)+5)'

In the denominator it has two terms.

So multiply and divide the term by its conjugate

'(sqrt(2)+3)/(sqrt(2)+5)''xx' '(sqrt(2)-5)/(sqrt(2)-5)'

'((sqrt(2)+3)*(sqrt(2)-5))/((sqrt(2)-5)*(sqrt(2)+5))'

Now use the foil method to simplify the numerator and use the formula a2-b2= (a+ b) (a-b)

'(sqrt(2)*sqrt(2)-5*sqrt(2)+3sqrt(2)-15)/(sqrt(2)^2 -5^2)'

'(2-2sqrt(2)-15)/(2-25)'

'(-2sqrt(2)-13)/(-23)'

Example 5 - Radical rationalized form:

Simplify the term '(sqrt(3)+3)/(sqrt(3)+5)'

Solution:

Given, '(sqrt(3)+3)/(sqrt(3)+5)'

In the denominator it has two terms.

So multiply and divide the term by its conjugate

'(sqrt(3)+3)/(sqrt(3)+5)' 'xx' '(sqrt(3)-5)/(sqrt(3)-5)'

'((sqrt(3)+3)*(sqrt(3)-5))/((sqrt(3)+5)*(sqrt(3)-5))'

Now use the foil method to simplify the numerator and use the formula a2-b2= (a+ b) (a-b)

'(sqrt(3)*sqrt(3)-5sqrt(3)+3sqrt(3)-15)/(sqrt(3)^2-25)'

'(3-2sqrt(3)-15)/(3-25)'

'(-2sqrt(3)-12)/(22)'

These are the examples of radical rationalized form

by: nitinp

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