Show that 1-3-8-1-8-7-1-7-6-1-6-5-1-5-2-5

1/(3 √(8)) 1/(√(8) √(7))+1/√(7) √(6) 1/√(6) √(5)+1/√(5) 2=5 Rationalise all the denominators, 3+√(8)/1 (√(8)+√(7))/1+√(7)+√(6)/1 (√(6)+√(5))/1+√(5)+2/1 =3+√(8̸ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Addition Rule of Differentiation

Show that 1/3...

Question

Show that $\frac{1}{(3 - \sqrt{8})} - \frac{1}{(\sqrt{8} - \sqrt{7})} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2} = 5$

Open in App

Solution

$\frac{1}{(3 - \sqrt{8})} - \frac{1}{(\sqrt{8} - \sqrt{7})} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2} = 5$
Rationalise all the denominators,
$\frac{3 + \sqrt{8}}{1} - \frac{(\sqrt{8} + \sqrt{7})}{1} + \frac{\sqrt{7} + \sqrt{6}}{1} - \frac{(\sqrt{6} + \sqrt{5})}{1} + \frac{\sqrt{5} + 2}{1} = 3 + \sqrt{/ 8} - \sqrt{/ 8} - \sqrt{/ 7} + \sqrt{/ 7} + \sqrt{/ 6} - \sqrt{/ 6} - \sqrt{/ 5^{1}} + \sqrt{/ 5} + 2 = 5$

Suggest Corrections

176

Show that 1(3−√8)−1(√8−√7)+1√7−√6−1√6−√5+1√5−2=5

1(3−√8)−1(√8−√7)+1√7−√6−1√6−√5+1√5−2=5 Rationalise all the denominators, 3+√81−(√8+√7)1+√7+√61−(√6+√5)1+√5+21=3+√/8−√/8−√/7+√/7+√/6−√/6−√/51+√/5+2=5

Show that $\frac{1}{(3 - \sqrt{8})} - \frac{1}{(\sqrt{8} - \sqrt{7})} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2} = 5$