Question

Rationalise 3√7+2√5 upon 3√7-2√5​

Answer 1

Answer:

83+12√35/43

Step-by-step explanation:

(3√7+2√5 )/( 3√7-2√5)

=[(3√7+2√5 )/( 3√7-2√5)]×[(3√7+2√5)/(3√7+2√5)]

=(3√7+2√5)^2/(3√7)^2-(2√5)^2

=(3√7)^2 + (2√5)^2 +2(3√7)(2√5)/63-20

=63+20+12√35/43

=83+12√35/43

Answer 2

Answer:

Method used:-

Rationalising denominator

Used Formula:-

$\mathtt{(a + b)(a - b) = {a}^{2} - {b}^{2} }$

Required Answer:-

$\mathtt{ \frac{83 + 12 \sqrt{35} }{43} }$

Solution:-

$\mathtt{ \frac{ = 3 \sqrt{7} + 2 \sqrt{5} }{3 \sqrt{7} - 2 \sqrt{5} } \times \frac{3 \sqrt{7} + 2 \sqrt{5} }{3 \sqrt{7} + 2 \sqrt{5} } }$

$\mathtt{ = \frac{3 \sqrt{7}(3 \sqrt{7} + 2 \sqrt{5} ) + 2 \sqrt{5}(3 \sqrt{7} + 2 \sqrt{5)} }{ {(3 \sqrt{7}) }^{2} - {(2 \sqrt{5} ) }^{2} } }$

$\mathtt{ = \frac{(3 \sqrt{7)^{2} } + 3 \sqrt{7} \times 2 \sqrt{5} + 2 \sqrt{5} \times 3 \sqrt{7} + {(2 \sqrt{5} )}^{2} }{ {(3 \sqrt{7}) }^{2} - {(2 \sqrt{5} )}^{2} } }$

$\mathtt{ = \frac{63 + 6 \sqrt{35 } + 6 \sqrt{35} + 20}{63 - 20} }$

$\mathtt{ = \frac{63 + 20 + 6 \sqrt{35} + 6 \sqrt{35} }{43} }$

$\mathtt{ = \frac{83 + 12 \sqrt{35} }{43} }$

Step-by-step explanation:

I hope this helps you mate