Question

Which of the following is true about the expression 7 + √3?

A. It represents the sum of a rational and irrational number and is equivalent to a rational number.B. It represents the sum of a rational and irrational number and is equivalent to an irrational number.C. It represents the sum of two rational numbers and is equivalent to a rational number. D. It represents the sum of two irrational numbers and is equivalent to an irrational number.

Answer 1

A. sum of rational and irrational and it ends up being rational

Answer 2

B. It represents the sum of a rational and irrational number and is equivalent to an irrational number.

Explanation:

Since 7 is a rational number and √3 is an irrational number.

Also Sum of rational number and irrational number is always a irrational number.

Thus, Option (B) is only correct answer.

Further, The number which is in the form of
`(p)/(q)`, where q≠0 is known as Rational Number. Also, here p & q are integers.

The number which is non-terminating and non-repeating decimal expansion is known as Irrational number. All real numbers except the rational number is an Irrational number.

Also we can not write an irrational number in a simple fraction.

Example: √2, 6.4589845,π,...., etc.