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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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:
Example: `root(5)(9)` `xx` `root(5)(2)` =
`root(5)(18)`
Distributive law:
Example: x (y + z) = xy + xz
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.
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)`