Question

Without solving, will the sum of 4.2+36−−√
be rational or irrational? Enter 1 for rational. Enter 2 for irrational. (1 point)

Answer 1

What must be true about a/b
if c/d
and ad+bc/bd
are both rational numbers? Enter 1 for option 1 and 2 for option 2.

Option 1: a/b
is rational

Option 2: a/b
is irrational

(1 point)

Answer 2

To determine whether the sum \( 4.2 + \sqrt{36} \) is rational or irrational, we first evaluate the square root:

\[
\sqrt{36} = 6
\]

Now, we can rewrite the expression:

\[
4.2 + \sqrt{36} = 4.2 + 6
\]

Calculating this gives:

\[
4.2 + 6 = 10.2
\]

Since \( 10.2 \) is a decimal representation of a rational number (it can be expressed as \( \frac{102}{10} \) or \( \frac{51}{5} \)), the sum is rational.

Therefore, the answer is:

**1** (for rational).