Question

simplify the following​

Answer 1

Simplify

(i)

${\implies \sf\sqrt{50 } - \sqrt{98} + \sqrt{162} }$

${\implies\sf\sqrt{2 \times {5}^{2} } - \sqrt{2 \times {7}^{2} } + \sqrt{2 \times {3}^{4} }}$

${\implies\sf\sqrt{ {5}^{2} \times 2 } - \sqrt{ {7}^{2} \times 2 } + \sqrt{ {3}^{4} \times 2}}$

${\implies{\sf\sqrt{ {5}^{2} } \times \sqrt{2} - \sqrt{ {7}^{2} } \times \sqrt{2} + \sqrt{ {3}^{4} } \times \sqrt{2} }}$

${\implies{\sf {5}^{ \frac{2}{2} } \times \sqrt{2} - {7}^{ \frac{2}{2} } \times \sqrt{2} + {3}^{ \frac{2}{2} } \times \sqrt{2} }}$

${\implies{ \sf{5}\times \sqrt{2} - {7} \times \sqrt{2} + { {3}^{2} } \times \sqrt{2}} }$

${\implies{ \sf{5}\times \sqrt{2} - {7} \times \sqrt{2} + { 9 } \times \sqrt{2} }}$

${{\implies\sf {5} \sqrt{2} - {7} \sqrt{2} + { 9 } \sqrt{2}} }$

${\implies{\sf {14} \sqrt{2} - {7} \sqrt{2}} }$

$\implies{ \bf{ \pink{ {7} \sqrt{2} }}}$

(ii)

${\implies\sf {2 \sqrt{50} \times 3 \sqrt{32} \times 4 \sqrt{18} }}$

${{\implies\sf2 \sqrt{2 \times {5}^{2} } \times 3 \sqrt{ {2}^{5} } \times 4 \sqrt{2 \times {3}^{2} } }}$

${\implies{\sf2(5 \times \sqrt{2} ) \times 3(4 \times \sqrt{2}) \times 4 (3 \times \sqrt{2} )} }$

${{\implies\sf2(5 \times \sqrt{2} ) \times 12 \sqrt{2} \times 12 \sqrt{2}} }$

${\implies{\sf2(5 \times \sqrt{2} ) \times 144( \sqrt{2} \times \sqrt{2}) }}$

${\implies{\sf2(5 \times \sqrt{2} ) \times 144 \times 2 } }$

${\implies{\sf2(5 \times \sqrt{2} ) \times 288 }}$

${\implies{\sf10 \sqrt{2} \times 288 } }$

${ {\implies \bf{ \pink{2880 \sqrt{2} }}} }$

Hope It Helpful ❣️

Answer 2

$\huge\pink{\boxed{\green{\mathfrak{\overbrace{\underbrace{\fcolorbox{red}{aqua}{\underline{\pink{✯Answer✯}}}}}}}}}$

(i)

√50-√98-√162

=√25 × √2 - √49 × √2 - √81 × √2

=5√2 - 7√2 - 9√2

-11√2(Ans).