Question

Solve and Rationalising 1/7 + 3√2

Answer 1

Solution

$\longrightarrow \tt \dfrac{1}{7 + 3 \sqrt{2} }$

$\sf \longrightarrow \dfrac{1}{7 + 3 \sqrt{2} } \times \dfrac{7 - 3 \sqrt{2} }{7 - 3 \sqrt{2} }$

$\sf \longrightarrow \dfrac{7 - 3 \sqrt{2} }{(7)^{2} - (3 \sqrt{2}) ^{2} }$

$\sf \longrightarrow \dfrac{7 - 3 \sqrt{2} }{49 -( 9 \times 2)}$

$\sf \longrightarrow \dfrac{7 - 3 \sqrt{2} }{49 -18}$

$\sf \longrightarrow \dfrac{7 - 3 \sqrt{2} }{31}$

Some Important Identities

• $\dag \: \sf {(a+b)^{0} = 1} \: \dag$

• $\dag \: \sf {(a+b)^{1} = a + b} \: \dag$

• $\dag \: \sf {(a+b)^{2} = a^{2} + 2ab + b^{2}} \: \dag$

• $\dag \: \sf {(a-b)^{2} = a^{2} - 2ab + b^{2}} \: \dag$

• $\dag \: \sf {a^{2} - b^{2} = (a+b)(a-b)} \: \dag$

Answer 2

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$\sf : \implies \dfrac{1}{7 + 3 \sqrt{2} }$

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$\sf : \implies \dfrac{1}{7 + 3 \sqrt{2} } \times \dfrac{7 - 3 \sqrt{2} }{7 - 3 \sqrt{2} }$

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$\sf : \implies \dfrac{7 - 3 \sqrt{2} }{ {(7)}^{2} - {(3 \sqrt{2}) }^{2} }$

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$\sf : \implies \dfrac{7 - 3 \sqrt{2} }{49 - 18}$

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$\sf : \implies \dfrac{7 - 3 \sqrt{2} }{31}$

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IdentitY used :-

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$\large : \implies \sf a^2 - b^2 =( a+b) ( a - b )$