Question

is the number \\(\sqrt{37} + -7\\) rational or irrational? \
rational \
irrational \
submit

Explanation:

Step1: Recall properties of irrational numbers

A rational number can be expressed as \(\frac{p}{q}\) where \(p,q\) are integers and \(q
eq0\). An irrational number is a real number that cannot be expressed as such a fraction. Also, the sum of a rational number and an irrational number is irrational.

Step2: Analyze \(\sqrt{37}\)

\(37\) is not a perfect square (since \(6^2 = 36\) and \(7^2=49\)), so \(\sqrt{37}\) is an irrational number.

Step3: Analyze \(- 7\)

\(-7\) is a rational number (it can be written as \(\frac{-7}{1}\)).

Step4: Determine the nature of \(\sqrt{37}+(-7)\)

Since \(\sqrt{37}\) is irrational and \(-7\) is rational, their sum ( \(\sqrt{37}-7\) which is the same as \(\sqrt{37}+(-7)\)) is irrational (because the sum of a rational and an irrational number is irrational).

Answer:

irrational