Question

3 root 40 + 3 root 39 by 3 root 41 - 3 root 40​

Answer 1

$\frac{3 \sqrt{40} + 3 \sqrt{39}}{3 \sqrt{41} - 3 \sqrt{40} }$

$On \: rationalizing \: denominator,$

$\frac{3 \sqrt{40} + 3 \sqrt{39} }{3 \sqrt{41} - 3 \sqrt{40} } \times \frac{3 \sqrt{41} + 3 \sqrt{40} }{3 \sqrt{41} + 3 \sqrt{40} }$

$\frac{(3 \sqrt{40} + 3 \sqrt{39} )(3 \sqrt{41} + 3 \sqrt{40} )}{369 - 360}$

$\frac{9( \sqrt{1640} + \sqrt{1600} + \sqrt{1599} + 1560)}{9}$

$2 \sqrt{410} + 40 + \sqrt{1599} + 2 \sqrt{390}$

$2( 20 + \sqrt{410} + 390) + \sqrt{1599}$