Question

Write the values of the following:

(1) $-\sqrt{9}$
(2) $\sqrt{25}$
(3) $-\sqrt{25}$
(4) $-\sqrt{121}$
(5) $\sqrt{100}$

Answer 1

$$\begin{gathered} \left(1\right)\mathrm{We}\mathrm{know}\mathrm{that}{3}^2=9\mathrm{and}{\left(-3\right)}^2=9 \\ \mathrm{Therefore},\mathrm{negative}\mathrm{square}\mathrm{root}\mathrm{of}9=-3 \\ \therefore -\sqrt{9}=-3 \end{gathered}$$

$$\begin{gathered} \left(2\right)\mathrm{We}\mathrm{know}\mathrm{that}{5}^2=25\mathrm{and}{\left(-5\right)}^2=25 \\ \mathrm{Therefore},\mathrm{positive}\mathrm{square}\mathrm{root}\mathrm{of}25=5 \\ \therefore \sqrt{25}=5 \end{gathered}$$

$$\begin{gathered} \left(3\right)\mathrm{We}\mathrm{know}\mathrm{that}{5}^2=25\mathrm{and}{\left(-5\right)}^2=25 \\ \mathrm{Therefore},\mathrm{negative}\mathrm{square}\mathrm{root}\mathrm{of}25=-5 \\ \therefore -\sqrt{25}=-5 \end{gathered}$$

$$\begin{gathered} \left(4\right)\mathrm{We}\mathrm{know}\mathrm{that}{11}^2=121\mathrm{and}{\left(-11\right)}^2=121 \\ \mathrm{Therefore},\mathrm{negative}\mathrm{square}\mathrm{root}\mathrm{of}121=-11 \\ \therefore -\sqrt{121}=-11 \end{gathered}$$

$$\begin{gathered} \left(5\right)\mathrm{We}\mathrm{know}\mathrm{that},{10}^2=100\mathrm{and}{\left(-10\right)}^2=100 \\ \mathrm{Therefore},\mathrm{positive}\mathrm{square}\mathrm{root}\mathrm{of}100=10 \\ \therefore \sqrt{100}=10 \end{gathered}$$