Question

select the best description for the sum of the expression below. $sqrt{10} + sqrt{26}$
a. neither rational nor irrational
b. both rational and irrational
c. rational
d. irrational

Explanation:

Step1: Identify type of $\sqrt{10}$

$\sqrt{10}$ is irrational (10 is not a perfect square, its decimal expansion is non-terminating and non-repeating).

Step2: Identify type of $\sqrt{26}$

$\sqrt{26}$ is irrational (26 is not a perfect square, its decimal expansion is non-terminating and non-repeating).

Step3: Sum of two such irrationals

The sum of two non-like irrational numbers (here, $\sqrt{10}$ and $\sqrt{26}$ cannot be combined into a single radical, and their sum results in a non-terminating, non-repeating decimal) is irrational.

Answer:

D. irrational