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What type of number is the sum of √ 2 and (3-√ 2) ?
Question

What type of number is the sum of √ 2 and (3-√ 2) ?

A.

an irrational number

B.

a rational number

C.

neither rational nor irrational

D.

cannot be determined

Correct option is B

Given
First number = 2\sqrt{2}​​
Second number = 323 - \sqrt{2}​​

Formula Used
Addition of real numbers.
A rational number can be expressed as a fraction of two integers.

Solution
Find the sum of the two given numbers:
Sum = 2+(32)\sqrt{2} + (3 - \sqrt{2})​​
Sum = 22+3 \sqrt{2} - \sqrt{2} + 3​​
Sum = 3
Since 3 can be written as 31\frac{3}{1}​, it is an integer and therefore a rational number.

Final Answer
So the correct answer is (b)

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