Question

Rationalize the denominator 5 + 3 root 2/ 5- 3 root 2 = a+b root 2
answer full

Answer 1

Answer:

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } = a + b \sqrt{2} \\ \frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \times \frac{5 + 3 \sqrt{2} }{5 + 3 \sqrt{2} } = a + b \sqrt{2} \\ \frac{(5 + \sqrt{3} {}^{2} )}{5 {}^{2} - ( \sqrt{3}) {}^{2} } = a + b \sqrt{2} \\ \frac{25 + 3 + 10 \sqrt{3} }{25 - 3} = a + b \sqrt{2} \\ \frac{28 + 10 \sqrt{3} }{22} = a + b \sqrt{2} \\ a \: = \frac{28}{22} \: and \: b = \frac{10}{22} \\ a \: = \frac{14}{11} \: and \: b \: = \frac{5}{11}$

Answer 2

Answer:

Hey mate your answer is given below