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.

Step-by-step 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:

$\sqrt{4} + \sqrt{25}=2 + 5= 7$ The result is an integer

$7=\frac{7}{1}$

$\sqrt{4} + \sqrt{9}= 2 + 3=5$ The result is an integer

$5=\frac{5}{1}$