See the solution process below: Explanation: Factor \displaystyle\sqrt{{{3}}} from the first three terms: \displaystyle{\left({2}-{2}-{4}\right)}\sqrt{{{3}}}+{5} \displaystyle-{4}\sqrt{{{3}}}+{5} ...

Antoine Apr 3, 2015 \displaystyle\sqrt{{{12}}}+{5}\sqrt{{{8}}}-{7}\sqrt{{{20}}}\equiv\sqrt{{{4}\cdot{3}}}+{5}\sqrt{{{4}\cdot{2}}}-{7}\sqrt{{{4}\cdot{5}}} \displaystyle\equiv\sqrt{{{4}}}\cdot\sqrt{{{3}}}+{5}\sqrt{{{4}}}\cdot\sqrt{{{2}}}-{7}\sqrt{{{4}}}\cdot\sqrt{{{5}}} ...

With difficulty...... \displaystyle{12}\sqrt{{7}} Explanation: As with fractions, we factorize the individual expressions and look for common terms. \displaystyle\sqrt{{{63}}}+\sqrt{{{175}}}+\sqrt{{{112}}} ...

You can rewrite these roots as a number multiplied by the root of tree. Explanation: \displaystyle\sqrt{{{75}}} + \displaystyle\sqrt{{{48}}} - \displaystyle\sqrt{{{243}}} = \displaystyle\sqrt{{{3}\cdot{25}}} ...

\displaystyle={5}{\left(\sqrt{{5}}+\sqrt{{2}}\right)} Explanation: You can multiply the brackets using the distributive law, in exactly the same way as in cases such as: \displaystyle{\left({x}+{3}\right)}{\left({x}-{4}\right)}={x}^{{2}}-{4}{x}+{3}{x}-{12} ...

\displaystyle{6}\sqrt{{{2}}} or about \displaystyle{8.485} Explanation: I'm not sure whether you want the answer in radical form (i.e. \displaystyle{6}\sqrt{{{2}}} ) or decimal form ...