Question

sort the square roots into rational or irrational.
drag & drop the answer
√81
√12
√36
√50
irrational
rational

Explanation:

Step1: Recall rational/irrational def

A rational number is a square root of a perfect square (integer result). Irrational: non - perfect square, non - repeating/non - terminating decimal.

Step2: Analyze \(\boldsymbol{\sqrt{81}}\)

\(\sqrt{81} = 9\) (since \(9\times9 = 81\)), so it's rational.

Step3: Analyze \(\boldsymbol{\sqrt{12}}\)

\(12\) is not a perfect square. \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{3}\) is irrational, so \(\sqrt{12}\) is irrational.

Step4: Analyze \(\boldsymbol{\sqrt{36}}\)

\(\sqrt{36}=6\) (since \(6\times6 = 36\)), so it's rational.

Step5: Analyze \(\boldsymbol{\sqrt{50}}\)

\(50\) is not a perfect square. \(\sqrt{50} = 5\sqrt{2}\), \(\sqrt{2}\) is irrational, so \(\sqrt{50}\) is irrational.

Answer:

Irrational: \(\sqrt{12}\), \(\sqrt{50}\)
Rational: \(\sqrt{81}\), \(\sqrt{36}\)