Question

add (6√7-1/2√2+2/3√5) + (1/3√5+3/2√2-√7)​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

$\sf\implies \bigg(6 \sqrt{7} - \dfrac{1}{2 \sqrt{2} } + \dfrac{2}{3 \sqrt{5} } \bigg) + \bigg( \dfrac{1}{3 \sqrt{5} } + \dfrac{3}{2 \sqrt{2} } - \sqrt{7} \bigg)$

Firstly we'll open the brackets and expanding the values.

Remember:The sign of values inside the brackets will change while opening the brackets

$\sf\implies6 \sqrt{7} - \dfrac{1}{2 \sqrt{2} } + \dfrac{2}{3 \sqrt{5} } + \dfrac{1}{3 \sqrt{5} } + \dfrac{3}{2 \sqrt{2} } - \sqrt{7}$

Now, make the same values together so that we can add or substract them easily.

$\sf\implies6 \sqrt{7} - \sqrt{7} - \dfrac{1}{2 \sqrt{2} } + \dfrac{3}{2 \sqrt{2} } + \dfrac{2}{3 \sqrt{5} } + \dfrac{1}{3 \sqrt{5} }$

$\sf\implies5 \sqrt{7} + \dfrac{2}{2 \sqrt{2} } + \dfrac{3}{3 \sqrt{5} }$

$\sf\implies5 \sqrt{7} + \dfrac{ \sqrt{2} \times \sqrt{2} }{2 \sqrt{2} } + \dfrac{3}{3 \sqrt{5} }$

$\sf\implies5 \sqrt{7} + \dfrac{ \sqrt{2} }{2} + \dfrac{1}{ \sqrt{5} }$

$\sf\implies5 \sqrt{7} + \dfrac{ \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } + \dfrac{1}{ \sqrt{5} }$

$\sf\implies5 \sqrt{7} + \dfrac{1}{ \sqrt{2} } + \dfrac{1}{ \sqrt{5} }$