Question

only 1st
please give solve on paper. ....
no ackward answer​

Answer 1

above is your answer mate

Answer 2

To do :

• Rationalise the denominator

What it actually means?

• To rationalize a denominator means to change the irrational denominator into a rational one .
• Most of the times this irrational denominator is in square root and hence to change it into rational , we multiply the numerator as well as denominator of the fraction by the similar square root.
• If the denominator consists two or more terms , both numerator and denominator are multiplied with the same digits except that the sign between the terms are reversed .
• For example : If denominator is 2+√3 , both numerator and denominator will be multiplied by 2-√3 .

$1. \: \: \tt\dfrac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} }$

$\tt \dfrac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \dfrac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ \\ \tt = \frac{(7 + 3 \sqrt{5})^{2} }{ {7}^{2} - (3 \sqrt{5})^{2} } \\ \\ \tt = \frac{49 + 45 + 42 \sqrt{5} }{49 - 45} \\ \\ \tt = \frac{94 + 42 \sqrt{5} }{4} \\ \\ \tt = \frac{2(47 + 21 \sqrt{5}) }{4} \\ \\ \boxed{\tt = \frac{47 + 21 \sqrt{5} }{2}}$

$\tt 2. \dfrac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ \tt = \frac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ \tt = \frac{(3 - 2 \sqrt{2} )^{2} }{ {3}^{2} - ( {2 \sqrt{2} ) ^{2} } } \\ \\ \tt = \frac{9 + 8 - 12 \sqrt{2} }{9 - 8} \\ \\ \tt = \frac{17 - 12 \sqrt{2} }{1} \\ \\ \boxed{\tt = 17 - 12 \sqrt{2} }$

$\tt 3. \dfrac{5 - 3 \sqrt{14} }{7 + 2 \sqrt{14} } \\ \\ \tt = \frac{5 - 3 \sqrt{14} }{7 + 2 \sqrt{14} } \times \frac{7 - 2 \sqrt{14} }{7 - 2 \sqrt{14} } \\ \\ \tt = \frac{5(7 - 2 \sqrt{14} ) - 3 \sqrt{14}(7 - 2 \sqrt{14}) }{ {7}^{2} - ( {2 \sqrt{14} }^{2} )} \\ \\ \tt = \frac{35 - 10 \sqrt{14} - 21 \sqrt{14} + 84}{49 - 56} \\ \\ \tt = \frac{119 - 31 \sqrt{14} }{ - 7} \\ \\ \boxed{\tt = \frac{ - 119 + 31 \sqrt{14} }{7}}$