Question

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Answer 1

$a)- \sqrt { 2 } \cdot ( - \sqrt { 4 \frac { 1 } { 2 } } )$

$\left(-\sqrt{2}\right)\left(-\sqrt{\frac{8+1}{2}}\right)$

$\left(-\sqrt{2}\right)\left(-\sqrt{\frac{9}{2}}\right)$

$\left(-\sqrt{2}\right)\left(-\frac{\sqrt{9}}{\sqrt{2}}\right)$

$\left(-\sqrt{2}\right)\left(-\frac{3}{\sqrt{2}}\right)$

$\left(-\sqrt{2}\right)\left(-\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)$

$\left(-\sqrt{2}\right)\left(-\frac{3\sqrt{2}}{2}\right)$

$\frac{\sqrt{2}\times 3\sqrt{2}}{2}$

$\frac{2\times 3}{2}$

$raspuns = > 3$

$b)\sqrt { \frac { 8 } { 15 } } \cdot \sqrt { 1 \frac { 1 } { 5 } }$

$\frac{\sqrt{8}}{\sqrt{15}}\sqrt{\frac{1\times 5+1}{5}}$

$\frac{2\sqrt{2}}{\sqrt{15}}\sqrt{\frac{1\times 5+1}{5}}$

$\frac{2\sqrt{2}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}\sqrt{\frac{1\times 5+1}{5}}$

$\frac{2\sqrt{2}\sqrt{15}}{15}\sqrt{\frac{1\times 5+1}{5}}$

$\frac{2\sqrt{30}}{15}\sqrt{\frac{1\times 5+1}{5}}$

$\frac{2\sqrt{30}}{15}\sqrt{\frac{5+1}{5}}$

$\frac{2\sqrt{30}}{15}\sqrt{\frac{6}{5}}$

$\frac{2\sqrt{30}}{15}\times \left(\frac{\sqrt{6}}{\sqrt{5}}\right)$

$\frac{2\sqrt{30}}{15}\times \left(\frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)$

$\frac{2\sqrt{30}}{15}\times \left(\frac{\sqrt{6}\sqrt{5}}{5}\right)$

$\frac{2\sqrt{30}}{15}\times \left(\frac{\sqrt{30}}{5}\right)$

$\frac{2\sqrt{30}\sqrt{30}}{15\times 5}$

$\frac{2\times 30}{15\times 5}$

$\frac{2\times 2}{5}$

$raspuns = > \frac{4}{5}=0.8$

$c)\sqrt{ 1 \frac{ 1 }{ 8 } } \times \sqrt{ 3 \frac{ 1 }{ 8 } }$

$\sqrt{\frac{8+1}{8}}\sqrt{\frac{3\times 8+1}{8}}$

$\sqrt{\frac{9}{8}}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{\sqrt{9}}{\sqrt{8}}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{3}{\sqrt{8}}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{3}{2\sqrt{2}}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{3\sqrt{2}}{2\times 2}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{3\sqrt{2}}{4}\sqrt{\frac{3\times 8+1}{8}}$

$\frac{3\sqrt{2}}{4}\sqrt{\frac{24+1}{8}}$

$\frac{3\sqrt{2}}{4}\sqrt{\frac{25}{8}}$

$\frac{3\sqrt{2}}{4}\times \left(\frac{\sqrt{25}}{\sqrt{8}}\right)$

$\frac{3\sqrt{2}}{4}\times \left(\frac{5}{\sqrt{8}}\right)$

$\frac{3\sqrt{2}}{4}\times \left(\frac{5}{2\sqrt{2}}\right)$

$\frac{3\sqrt{2}}{4}\times \left(\frac{5\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}\right)$

$\frac{3\sqrt{2}}{4}\times \left(\frac{5\sqrt{2}}{2\times 2}\right)$

$\frac{3\sqrt{2}}{4}\times \left(\frac{5\sqrt{2}}{4}\right)$

$\frac{3\sqrt{2}\times 5\sqrt{2}}{4\times 4}$

$\frac{3\times 2\times 5}{4\times 4}$

$\frac{3\times 5}{2\times 4}$

$\frac{15}{2\times 4}$

$raspuns = > \frac{15}{8}=1.875$

Sper ca ti-am fost de folos. Succes!!