91影视

(a) Explain why ${(-\sqrt{n})}^2$is always non-negative, for $n鈮�0$

(b) Explain why $-{\left(\sqrt{n}\right)}^2$ is always non-positive, for $n鈮�0$

Use the binomial square pattern to simplify ${(3+\sqrt{2})}^2$. Explain all your steps.

In the following exercise , simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{128}}{\sqrt{72}} \\ \left(ii\right)\frac{\sqrt[3]{128}}{\sqrt[3]{54}} \end{gathered}$$

In the following exercise simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{48}}{\sqrt{75}} \\ \left(ii\right)\frac{\sqrt[3]{81}}{\sqrt[3]{24}} \end{gathered}$$

In the following exercise simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{200m^5}}{\sqrt{98m}} \\ \left(ii\right)\frac{\sqrt[3]{54y^2}}{\sqrt[3]{2y^5}} \end{gathered}$$

In the following exercise simplify.

$$\begin{gathered} \left(i\right)\frac{\sqrt{108n^7}}{\sqrt{243n^3}} \\ \left(ii\right)\frac{\sqrt[3]{54y}}{\sqrt[3]{16y^4}} \end{gathered}$$

In the following exercise , simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{75r^3}}{\sqrt{108r^7}} \\ \left(ii\right)\sqrt[3]{\frac{24x^7}{81x^4}} \end{gathered}$$

In the following exercises, approximate each root and round to two decimal places .

In the following exercise , simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{196q}}{\sqrt{484q^5}} \\ \left(ii\right)\frac{\sqrt[3]{16m^4}}{\sqrt[3]{54m}} \end{gathered}$$

In the following exercise , simplify

$$\begin{gathered} \left(i\right)\frac{\sqrt{108p^5{q}^2}}{\sqrt{3p^3{q}^6}} \\ \left(ii\right)\frac{\sqrt[3]{-16a^4{b}^{-2}}}{\sqrt[3]{2a^{-2}b}} \end{gathered}$$