Question

which of the following is not a rational expression
1.√21 2.x+1/2 3.8√x+6√y 4.x+√2 / x-√2​

Answer 1

Answer:

I think all are not rational numbers excluding the 2nd one

Answer 2

Concept

A rational number is the one that can be expressed in the form p/q where p and q and not equal to 0.

Given

1.√21

2.x+1/2

3.8√x+6√y

4.x+√2 / x-√2

Find

we need to find the which of the given expressions is not a rational expression

Solution

1.√21

the square root of 21 is 4.5825756

This number is a non terminating decimal and hence cannot be expressed as a fraction.

Therefore, √21 is not rational

2. x+1/2

x+1/2 can be written as (2x+1)/2

The following expression will be rational for all real values of x

3. 8√x+6√y

if x and y are positive numbers, then only the expression will be rational.

4. x+√2 / x-√2

x+√2 / x-√2 = (x+√2)^2/( $x^{2} - 2$)

The given expression will be rational for all values of x

Thus, out of the given expressions √21  can never be rational

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