Question

Simplify:$\left(a\right)\sqrt{-169}$ $\left(b\right)-\sqrt{81}$

Short answer

The solutions of (a) is there is no real number and (b) is$-9$

Step-by-step solution

Part (a). Step 1. Given information

The root:$\sqrt{-169}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt{-169} \\ =\sqrt{-169}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{real}\mathrm{number} \end{gathered}$$

There is no real number whose square is $\sqrt{-169}$

Part (b) Step 1. Given information

The root:$-\sqrt{81}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} -\sqrt{81} \\ =-9 \end{gathered}$$

Since, $9^2=81$and the negative is in front of the radical sign.

Therefore, the solution is$-9$