Algebraic Operations - Radicals, 18

Category: Algebra, Arithmetic

"Published in Newark, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

The above equation can be written as

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. 

As a rule in Mathematics, all radicals in the denominator should be rationalized or eliminated. In this case, multiply both the numerator and the denominator by √2 so that √2 becomes 2 in the denominator as follows

Therefore, the final answer is

  

Algebraic Operations - Radicals, 17

Category: Algebra, Arithmetic

"Published in Newark, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

The above equation can be written as

As a rule in Mathematics, all radicals in the denominator should be rationalized or eliminated. In this case, multiply both the numerator and the denominator by √3 so that √3 becomes 3 in the denominator as follows 

Therefore, the final answer is

Algebraic Operations - Radicals, 16

Category: Algebra

"Published in Newark, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

If you will cube a radical in which the index is 3 or that have a cube root sign, then the cube root sign in the equation will be cancelled.  

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Apply the principles of Binomial Theorem or cubing of a binomial to the above equation as follows

 

Therefore, the final answer is