1. Simplify without using a 1.1. \( \sqrt{32}-\sqrt{8}+2 \sqrt{18} \) \( 1.2 . \frac{\sqrt{27 m^{6}}-\sqrt{48 m^{6}}}{\sqrt{12 m^{6}}} \) 1.3. \( (\sqrt{5}-2)^{2} \)

Calculate or simplify the expression \( \sqrt{32}-\sqrt{8}+2\sqrt{18} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{32}-\sqrt{8}+2\sqrt{18}\) - step1: Simplify the root: \(4\sqrt{2}-\sqrt{8}+2\sqrt{18}\) - step2: Simplify the root: \(4\sqrt{2}-2\sqrt{2}+2\sqrt{18}\) - step3: Simplify the root: \(4\sqrt{2}-2\sqrt{2}+2\times 3\sqrt{2}\) - step4: Multiply the terms: \(4\sqrt{2}-2\sqrt{2}+6\sqrt{2}\) - step5: Collect like terms: \(\left(4-2+6\right)\sqrt{2}\) - step6: Calculate: \(8\sqrt{2}\) Calculate or simplify the expression \( \frac{\sqrt{27m^{6}}-\sqrt{48m^{6}}}{\sqrt{12m^{6}}} \). Simplify the expression by following steps: - step0: Solution: \(\frac{\sqrt{27m^{6}}-\sqrt{48m^{6}}}{\sqrt{12m^{6}}}\) - step1: Simplify the root: \(\frac{3\sqrt{3}\times m^{3}-\sqrt{48m^{6}}}{\sqrt{12m^{6}}}\) - step2: Simplify the root: \(\frac{3\sqrt{3}\times m^{3}-4\sqrt{3}\times m^{3}}{\sqrt{12m^{6}}}\) - step3: Simplify the root: \(\frac{3\sqrt{3}\times m^{3}-4\sqrt{3}\times m^{3}}{2\sqrt{3}\times m^{3}}\) - step4: Subtract the terms: \(\frac{-\sqrt{3}\times m^{3}}{2\sqrt{3}\times m^{3}}\) - step5: Simplify the expression: \(\frac{-\sqrt{3}}{2\sqrt{3}}\) - step6: Reduce the fraction: \(\frac{-1}{2}\) - step7: Rewrite the fraction: \(-\frac{1}{2}\) Calculate or simplify the expression \( (\sqrt{5}-2)^{2} \). Calculate the value by following steps: - step0: Calculate: \(\left(\sqrt{5}-2\right)^{2}\) - step1: Expand the expression: \(\left(\sqrt{5}\right)^{2}-2\sqrt{5}\times 2+2^{2}\) - step2: Calculate: \(5-4\sqrt{5}+4\) - step3: Add the numbers: \(9-4\sqrt{5}\) The simplified expressions are: 1. \( \sqrt{32}-\sqrt{8}+2\sqrt{18} = 8\sqrt{2} \) 2. \( \frac{\sqrt{27m^{6}}-\sqrt{48m^{6}}}{\sqrt{12m^{6}}} = -\frac{1}{2} \) 3. \( (\sqrt{5}-2)^{2} = 9-4\sqrt{5} \)