Question

simplify the following expressions completely. enter dne if the answer is not a real number.
a) \\(\sqrt{36} = \\)
b) \\( -\sqrt{81} = \\)
c) \\(\sqrt{-16} = \\)

Explanation:

Part (a)

Step1: Recall square root definition

The square root of a number \( x \), denoted \( \sqrt{x} \), is a number \( y \) such that \( y^2 = x \). For \( \sqrt{36} \), we need to find a number whose square is 36.

Step2: Find the square root

We know that \( 6^2 = 36 \), so \( \sqrt{36}=6 \).

Part (b)

Step1: Simplify the square root first

First, find \( \sqrt{81} \). Since \( 9^2 = 81 \), \( \sqrt{81}=9 \).

Step2: Apply the negative sign

Now, we have \( -\sqrt{81} \), so we take the negative of the square root we found. Thus, \( -\sqrt{81}=-9 \).

Part (c)

Step1: Recall the domain of square root

The square root of a negative number is not a real number because for any real number \( y \), \( y^2\geq0 \). So, \( \sqrt{-16} \) has no real number solution.

Answer:

s:
a) \( \boldsymbol{6} \)
b) \( \boldsymbol{-9} \)
c) \( \boldsymbol{DNE} \)