after rationalizing the denominator of 7/3root3-2root2 we get the denominator as
Answers
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\begin{gathered} \frac{7}{3 \sqrt{3} - 2 \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{7}{3 \sqrt{3} - 2 \sqrt{2} } \times \frac{3 \sqrt{3} + 2 \sqrt{2} }{3 \sqrt{3} + 2 \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{7(3 \sqrt{3} + 2 \sqrt{2} ) }{ {(3 \sqrt{3} )}^{2} - {(2 \sqrt{2} )}^{2} } \\ \\ = \frac{7 \times 3 \sqrt{3} + 7 \times 2 \sqrt{2} }{27 - 8} \\ \\ = \frac{21 \sqrt{3} + 14 \sqrt{2} }{19} \end{gathered}
3
3
−2
2
7
onrationalizingthedenominatorweget
=
3
3
−2
2
7
×
3
3
+2
2
3
3
+2
2
usingtheidentity
(a+b)(a−b)=a
2
−b
2
=
(3
3
)
2
−(2
2
)
2
7(3
3
+2
2
)
=
27−8
7×3
3
+7×2
2
=
19
21
3
+14
2
Hope this helps!!!
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