Question

rationalize the denominator 2)√3-1​

Answer 1

Solution:

Given: 2/(√3 - 1)

We have to rationalise the denominator. Rationalization means to remove all the surds from the denominator part.

So,

$\tt \dfrac{2}{ \sqrt{3} - 1}$

$\tt = \dfrac{2 \times ( \sqrt{3} + 1)}{( \sqrt{3} - 1)( \sqrt{3} + 1)}$

Applying identity a² - b² = (a + b)(a - b), we get,

$\tt = \dfrac{2 \times ( \sqrt{3} + 1)}{3 - 1}$

$\tt = \dfrac{2 \times ( \sqrt{3} + 1)}{2}$

$\tt = \sqrt{3} + 1$

★ So, after rationalization, result we get = √3 + 1.

Answer:

• √3 + 1

•••♪

Answer 2

Correct Question:

Rationalize the denominator $\small \bf\dfrac{2}{ \sqrt{3} - 1}$

Step by step explanation:

$\sf \dashrightarrow \dfrac{2}{ \sqrt{3} - 1 }$

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

$\sf \dashrightarrow \dfrac{ 2(\sqrt{3} + 1) }{ ( \sqrt{3} - 1)( \sqrt{3} + 1) }$

$\sf \dashrightarrow \dfrac{ 2(\sqrt{3} + 1) }{ {( \sqrt{3})}^{2} - (1) {}^{2} }$

$\sf \dashrightarrow \dfrac{ 2(\sqrt{3} + 1) }{ {( \sqrt{3})}^{2} - 1}$

$\sf \dashrightarrow \dfrac{ 2(\sqrt{3} + 1) }{ { 3- 1} }$

$\sf \dashrightarrow \dfrac{ 2(\sqrt{3} + 1) }{ 2 }$

$\sf \dashrightarrow \dfrac{ \cancel2(\sqrt{3} + 1) }{ \cancel 2 }$

$\sf \dashrightarrow \dfrac{ (\sqrt{3} + 1) }{1}$

$\sf \dashrightarrow \sqrt{3} + 1$

$\purple \bigstar\blue{\boxed{ \gray { \sf{}Hence \: \: Rationalized}}} \purple \bigstar$

Explanation:

To rationalize the denominator we have to multiply it with same same number but by changing the signs

eg:(√3-√2)×(√3+√2)

=(√3)²-(√2)²

=3-2

=1

↑The same rule is applied above