Question

Given the two expressions shown below:

square root of 4 plus square root of 25
square root of 4 plus square root of 9

Which statement best describes the two expressions?
A. Both are rational.
B. Both are irrational.
C. A is rational, but B is irrational.
D. A is irrational, but B is rational.

Answer 1

Answer: A. Both are rational.

Explanation:

Although both expressions have square roots, the result of each square root is an integer, which can be expressed as a fraction.

In this sense:

Rational numbers are all numbers that can be represented as the quotient (division) of two integer numbers. This means they can be represented as a fraction in which the denominator is nonzero.

If we solve both expressions, we will be able to see that the result is an integer that can be expressed as a fraction with two integers:

`√(4) + √(25)=2 + 5= 7` The result is an integer

`7=(7)/(1)`

`√(4) + √(9)= 2 + 3=5` The result is an integer

`5=(5)/(1)`