Question

√3-√2/√3+√2 we have​

Answer 1

Answer:

1/5+2√6

Step-by-step explanation:

√3-√2/√3+√2

Multiply the numerator and denominator with √3+√2

Then,

√3-√2/√3+√2×√3+√2/√3+√2

(√3)^2-(√2)^2/(√3+√2)^2

3-2/(√3)^2+(√2)^2+2×√3×√2

3-2/3+2+2√6

1/5+2√6

Therefore,

√3-√2/√3+√2 = 1/5+2√6

HOPE THIS HELPS YOU!!!

Answer 2

ANSWER:

${ \bf{ \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }}$

Rationalizing the denominator

${ \tt{ \to \frac{ (\sqrt{3} - \sqrt{2} )( \sqrt{3} - \sqrt{2}) }{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2}) } }}$

Using

(a - b)(a - b) = (a - b)² = a² - 2ab + b²

(a + b)(a - b) = a² - b²

${ \tt{ \to \frac{ {( \sqrt{3} })^{2} - 2( \sqrt{2})( \sqrt{3}) + {( \sqrt{2}) }^{2} }{ {( \sqrt{3} )}^{2} - { (\sqrt{2} )}^{2} } }}$

${ \tt{ \to \frac{3 - 2 \sqrt{6} + 2 }{3 - 2} = \frac{5 - \sqrt{6} }{1} = 5 - \sqrt{6} }}$

Hence

${ \sf{ \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \implies5 - \sqrt{6} }}$

CONCEPTS USED:

♦ Surds

♦ Algebraic identities

MORE INFORMATION:

→ (a + b)² = a² + b² + 2ab

→ a² + b² = (a + b)² - 2ab

→ a² - b² = (a - b)(a + b)

→ (a - b)² = a² - 2ab + b²

→ (a + b)² + (a - b)² = 2(a² + b²)

→ (a + b)² - (a - b)² = 4ab