Evaluate:
$$\left( i \right)\,\,\,3\sqrt { - \frac{{512}}{{343}}} $$
$$\left( {ii} \right)\,\,\,3\sqrt {2.197} $$

Solution

(1)

$$\displaystyle3\sqrt {{{ - 512} \over {343}}}  = 3\sqrt {{{ - {{\left( 8 \right)}^3}} \over { + {{\left( 7 \right)}^3}}}}  = \root 3 \of {{{\left( {{{ - 8} \over 7}} \right)}^3}} $$

$$\displaystyle = {{ - 8} \over 7}$$

(ii)

$$\displaystyle3\sqrt {2.197} $$

$$\displaystyle = 3\sqrt {1.3 \times 1.3 \times 1.3} $$

$$ = 1.3$$