Question

which of these numbers are solutions of $n^2 = 36$? choose two correct answers. $-18$ $-9$ $-6$ $6$ $9$ $18$

Explanation:

Step1: Recall the square root property

For the equation \(n^2 = 36\), we can solve for \(n\) by taking the square root of both sides. Remember that if \(x^2=a\) (\(a\geq0\)), then \(x = \pm\sqrt{a}\).

Step2: Calculate the square roots

Applying the square root property to \(n^2 = 36\), we get \(n=\pm\sqrt{36}\). Since \(\sqrt{36} = 6\), then \(n = 6\) or \(n=- 6\). We can check by squaring these values: \((6)^2=36\) and \((-6)^2 = 36\), while \((-18)^2=324\), \((-9)^2 = 81\), \(9^2=81\), \(18^2 = 324\) which are not equal to 36.

Answer:

\(-6\), \(6\) (corresponding to the options: \(-6\) and \(6\))