To determine whether the sum \(4.2 + \sqrt{36} + 4.2 + \sqrt{36}\) is rational or irrational without solving it, we can analyze the components:
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\(4.2\) is a rational number because it can be expressed as a fraction, \( \frac{42}{10} \).
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\(\sqrt{36}\) is equal to \(6\), which is also a rational number.
Now, let's rewrite the expression: \[ 4.2 + \sqrt{36} + 4.2 + \sqrt{36} = 4.2 + 6 + 4.2 + 6 \]
To simplify: \[ 4.2 + 6 + 4.2 + 6 = (4.2 + 4.2) + (6 + 6) = 8.4 + 12 = 20.4 \]
Since \(20.4\) is a decimal that can also be expressed as a fraction \(\frac{204}{10}\), it is a rational number.
Therefore, the sum \(4.2 + \sqrt{36} + 4.2 + \sqrt{36}\) is rational.