Question

Rationalise the denominator and simplify 1 + √ 2 /3 + 2 √ 2

Answer 1

Answer:

answer is √2 - 1

Step-by-step explanation:

(1+√2)/(3 + 2√2)

= (1+√2)/(3+2√2) × (3-2√2)/(3-2√2)

= [(1+√2)(3-2√2)]/[(3)² - (2√2)²]

= [3 - 2√2 + 3 √2 - 4]/[9 - 8]

= [√2 - 1]/1

= √2 - 1

Answer 2

Answer:

$\huge\bigstar\:\underline{\boxed{\tt \: 7 + 5 \sqrt{2}} } \: \bigstar$

Step-by-step explanation:

$:\implies\:\sf \dfrac{1 + \sqrt{2}}{3 - 2 \sqrt{2}}$

$:\implies\:\sf \dfrac{1 + \sqrt{2}}{3 - 2 \sqrt{2}} \: \times \: \sf \dfrac{3 + 2 \sqrt{2}}{3 - 2 \sqrt{2}}$

$:\implies\:\sf \dfrac{3 + 2\sqrt{2} \: + \: 3 \sqrt{2} \: + \: 2 \sqrt{4} }{(3)^{2} - (2\sqrt{2})^{2} }$

$:\implies\:\sf \dfrac{3 + 5\sqrt{2} \: + \: 2 \: \times \: \sqrt{2 \: \times \: 2} }{9 \: - \: 4\: \times \: 2 }$

$:\implies\:\sf \dfrac{3 \: + \: 5\sqrt{2} \: + \: 2 \: \times \: 2 }{9 \: - \: 4 \: \times \: 2 }$

$:\implies\:\sf \dfrac{3 \: + \: 5\sqrt{2} \: + \: 4 }{9 \: - \: 8}$

$:\implies\:\sf \dfrac{3 \: + \: 5\sqrt{2} \: + \: 4 }{1}$

$: \implies {\underline{\boxed{\sf \: \: 7 + 5 \sqrt{2}}} } \: \: \: \bigg \lgroup \: \bf{Required \: Answer} \: \bigg \rgroup$