Examine, whether the following numbers are rational or irrational: `sqrt(3)+sqrt(2)` (v) `sqrt(3)+sqrt(5)` (vi) `(sqrt(2)-2)^2`

Explanation

`(iv) √3 + √2`
Here, `sqrt3` is a irrational number and `sqrt2` is an irrational number.
We know that, the sum of two irrational numbers is an irrational number.
Hence ,` sqrt3 + sqrt2` is an irrational number.
`(v) sqrt3 + sqrt5`
Here, `sqrt3` is a irrational number and `sqrt5` is an irrational number.
We know that, the sum of two irrational numbers is an irrational number.
Hence , `sqrt3 + sqrt5 `is an irrational number.
`(vi) (sqrt2 – 2)^2`
`(sqrt2 – 2)^2= sqrt2^2 + 2^2 –2 xx sqrt2 xx 2`
`[(a - b)^2 = a^2 + b^2- 2ab]`
` 2 + 4 - 4sqrt2`
`6 - 4 sqrt2`
Here, `6` is a rational number and `4sqrt2` is an irrational number.
We know that, the sum of a rational and irrational number is an irrational number.
Hence, `(sqrt2 – 2)^2` is an irrational number."