Question

rationalize the denominator of. 3/3 - 2√2​

Answer 1

$\Large {\underline { \sf \orange{Explication \: Of \: Steps :}}}$

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf{ \dfrac{9+ 6 \sqrt{2} }{ 9 - ( 4 \times 2)}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf{ \dfrac{9+ 6 \sqrt{2} }{ 9 - ( 8)}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \boxed{\sf{ 9+ 6 \sqrt{2} }}$

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❝ So, the answer is 9 + 6√2 is the answer. ❞

$\Large {\underline { \sf \orange{More \: Identities :}}}$

• (√a)² = a

• √a√b = √ab

• √a/√b = √a/b

• (√a + √b)(√a - √b) = a - b

• (a + √b)(a - √b) = a² - b

• (√a ± √b)² = a ± 2√ab + b

• (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd