Introduction to Simplifying Products of Radicals

In mathematics, the radicals are considered as one of the important topic. Radical numbers, which are having the root of square are called as radicals. It can have all types of roots. Index number is always given in the radicals. The symbols which are used in the radicals as symbol for symbol. The number which is inside the given root is called as radicand number. For example, `root(7)(15)` are known as the radicals.

 

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Explanation to Simplifying Products of Radicals

 

The explanations given for simplifying the products of the given radicals are given below,

Radicals consists of mainly two types. They are given below the following section,

 

Products law for radicals:

  • For the radicals the products law is also used.
  • The products is law used only we are having the same index value. Then the multiplication are made to the inside values. 

 

Example:  `root(5)(9)`  `xx`   `root(5)(2)`   =  `root(5)(18)` 

Distributive law:

  • For the radicals the distributive law is also used.
  • the multiplication are made to each and every term present in the given radicals. 

Example:  x (y + z) = xy + xz

Example Problems to Simplifying Products of Radicals

 

Problem 1: Simplify the product of the following radicals, `sqrt(13)`  and   `sqrt(13)` .

Solution:

Step 1: The given radicals for finding the product are as follows,

`sqrt(13)`   `xx`   `sqrt(13)`

Step 2: For the above terms we have to find the product and then we are simplifying,

`sqrt(169)`

= 13

This is the obtained answer for simplifying the radicals.

 

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Problem 2: Simplify the product of the following radicals, `5(sqrt(2)+sqrt(7))`  and   `5(sqrt(7)+sqrt(2))` .

Solution:

Step 1: The given radicals for finding the product are as follows,

`5(sqrt(2)+sqrt(7))`  and   `5(sqrt(7)+sqrt(2))` .

Step 2: For the above terms we have to find the product and then we are simplifying,

`5(sqrt(2)+sqrt(7))`  and   `5(sqrt(7)+sqrt(2))` .

= 5`sqrt(2) + sqrt(7)`    `xx`  5 `sqrt(7)` + 5 `sqrt(2)`

= 5 `sqrt(14)`  `xx`  5 `sqrt(14)`

= 5 `sqrt(196)`

=  5 `xx`  14

= 70

This is the obtained answer for simplifying the radicals.


Practice Problems to Simplifying Products of Radicals

 

Problem 1: Simplify the product of the following radicals, `sqrt(12)`  and   `sqrt(13)` .

Answer: 156

Problem 2: Simplify the product of the following radicals,`4(sqrt(4)+sqrt(6))`  and `4(sqrt(6)+sqrt(4))` .

Answer: 4`sqrt(576)`