Question

1 by root 15 + 4 root 14 + 2 by root 12minus 2root 35 minus 3 by root 13 minus 4 root 10​

Answer 1

Answer:

1+15 +3+14+2+/12-2+35-3 by root 13. - 4/10

Answer 2

$\frac{\sqrt{15} +210\sqrt{14} +90 +30\sqrt{490} -5\sqrt{13}-20\sqrt{10} }{15}$ is the rationalization of the given number.

Given:

$\frac{1}{\sqrt{15} } + \frac{4\sqrt{14 }+2 }{12 - 2\sqrt{35} } - \frac{3}{\sqrt{13}-4\sqrt{10} }$

To Find:

The rationalization of the given number.

Solution:

$\frac{1}{\sqrt{15} } + \frac{4\sqrt{14 }+2 }{12 - 2\sqrt{35} } - \frac{3}{\sqrt{13}-4\sqrt{10} }$

=$\frac{1}{\sqrt{15} }*\frac{\sqrt{15 }}{\sqrt{15} } + \frac{4\sqrt{14 }+2 }{12 - 2\sqrt{35} }*\frac{12 +2\sqrt{35}}{12 +2\sqrt{35}} - \frac{3}{\sqrt{13}-4\sqrt{10} }*\frac{\sqrt{13}+4\sqrt{10}}{\sqrt{13}+4\sqrt{10}}$

= $\frac{\sqrt{15}}{ 15} + \frac{(4\sqrt{14 }+2 )(12 +2\sqrt{35})}{12^{2} - (2\sqrt{35})^{2} } - \frac{3*\sqrt{13}+4\sqrt{10}}{\sqrt{13}^{2} -(4\sqrt{10} )^{2} }$

 = $\frac{\sqrt{15}}{ 15} + \frac{(4\sqrt{14 }*12+2*12 +2\sqrt{35}*4\sqrt{14 }+ 2*4\sqrt{14 })}{144 - 140 } - \frac{3*\sqrt{13}+3*4\sqrt{10}}{169 -160 }$

= $\frac{\sqrt{15}}{ 15} + \frac{(48\sqrt{14 }+24 +8\sqrt{490}+ 8\sqrt{14 })}{4 } - \frac{3\sqrt{13}+12\sqrt{10}}{9 }$

= $\frac{\sqrt{15}}{ 15} + 4*\frac{(14\sqrt{14 }+6 +2\sqrt{490})}{4 } - 3*\frac{\sqrt{13}+4\sqrt{10}}{9 }$

= $\frac{\sqrt{15}}{ 15} + \frac{(14\sqrt{14 }+6 +2\sqrt{490})}{1} - \frac{\sqrt{13}+4\sqrt{10}}{3 }$

= $\frac{\sqrt{15} +210\sqrt{14} +90 +30\sqrt{490} -5\sqrt{13}-20\sqrt{10} }{15}$

∴ $\frac{\sqrt{15} +210\sqrt{14} +90 +30\sqrt{490} -5\sqrt{13}-20\sqrt{10} }{15}$ is the rationalization of the given number.

#SPJ3