Sum of Two Irrational Numbers

Introduction to sum of two irrational numbers:

Let us study about sum of two irrational numbers. Irrational numbers are defined as the numbers which cannot be written in the form of simple ratios of two integers.
The irrational numbers are commonly said to have infinite values. These irrational numbers can get added with each other by approximating or rounding those infinite values to some nearest values.
Some examples for sum of two irrational numbers are discussed below.

Two Irrational Numbers:

Two irrational numbers – example 1:

Add the following two irrational numbers 3.4256… and 2.3227…


Solution:

The two given irrational numbers are 3.4256… and 2.3227…
To add the two given irrational numbers follow the steps below given steps:
3.426 + 2.323 (by rounding the values with three decimal points)
Therefore the added value of the two given irrational number is found to be as ‘5.749’


Two irrational numbers – example 2:

Add the following two irrational numbers 0.436… and 12.987…


Solution:

The two given irrational numbers are 0.436… and 12.987…
To add the two given irrational numbers follow the steps below given steps:
0.44 + 12.99 (by rounding the values with two decimal points)
Therefore the added value of the two given irrational number is found to be as ’13.43’
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Two irrational numbers – example 3:

Add the following two irrational numbers `sqrt(3) and sqrt(12)`


Solution:

The two given irrational numbers are `sqrt(3) and sqrt(12)`
To add the two given irrational numbers follow the steps below given steps:
`sqrt(3) + sqrt(12) `
`sqrt(15)` = 3.872983…
3.873 (round the values with three decimal points)
Therefore the added value of the two given irrational number is found to be as ‘3.873’


Two irrational numbers – example 4:

Add the following two irrational numbers 6.2328… and `sqrt(8)`


Solution:

The two given irrational numbers are 6.2328… and `sqrt(8)`
To add the two given irrational numbers follow the steps below given steps:
6.2328… + `sqrt(8)`
6.2328… + 2.8284…
6.233 + 2.828 (by rounding the values with three decimal points)
Therefore the added value of the two given irrational number is found to be as ‘9.061’
Two irrational numbers – exercises:

Add the following two irrational numbers `sqrt(2) and sqrt(6).` (Answer: 3.863)
Add the following two irrational numbers 0.2028… and 9.45454... (Answer: 9.658)