1.

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

Answer»

\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} }


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