Solve- 1-2-3-3-12-3-2-13-2-2-

1/√(2)+√(3) √(3)+1/2+√(3)+√(2)+1/3+2√(2) Rationalize all the terms = √(2) √(3)/ 1 2√(3) 3+2 √(3)/1+3√(2) 4+3 2√(2)/1 = √(3) √(2) 2√(3)+3 2+√(3)+3√ ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Solve: 1√2+√...

Question

Solve:
$\frac{1}{\sqrt{2} + \sqrt{3}} - \frac{\sqrt{3} + 1}{2 + \sqrt{3}} + \frac{\sqrt{2} + 1}{3 + 2 \sqrt{2}}$ .

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Solution

$\frac{1}{\sqrt{2} + \sqrt{3}} - \frac{\sqrt{3} + 1}{2 + \sqrt{3}} + \frac{\sqrt{2} + 1}{3 + 2 \sqrt{2}}$
Rationalize all the terms
$= \frac{\sqrt{2} - \sqrt{3}}{- 1} - \frac{2 \sqrt{3} - 3 + 2 - \sqrt{3}}{1} + \frac{3 \sqrt{2} - 4 + 3 - 2 \sqrt{2}}{1}$
$= \sqrt{3} - \sqrt{2} - 2 \sqrt{3} + 3 - 2 + \sqrt{3} + 3 \sqrt{2} - 4 + 3 - 2 \sqrt{2}$
$= 0$

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Solve:1√2+√3−√3+12+√3+√2+13+2√2.

1√2+√3−√3+12+√3+√2+13+2√2Rationalize all the terms=√2−√3−1−2√3−3+2−√31+3√2−4+3−2√21=√3−√2−2√3+3−2+√3+3√2−4+3−2√2=0

Solve:
$\frac{1}{\sqrt{2} + \sqrt{3}} - \frac{\sqrt{3} + 1}{2 + \sqrt{3}} + \frac{\sqrt{2} + 1}{3 + 2 \sqrt{2}}$ .