Question

rationalise the denominator 2/√3-1​

Answer 1

Answer:

To rationalize the denominator we must multiply and divide the number by the denominator's conjugate. Conjugate of denominator is -- 2 + √3. We know that, (a+b) ( a-b) = a² - b². So, (2+√3)(2-√3) = 2² -(√3)² = 4 - 3 = 1.

Answer 2

The answer is 1.

Given:

$\frac{2}{\sqrt{3}-1 }$

To Find:

We have to rationalize the denominator $\frac{2}{\sqrt{3}-1 }$.

Solution:

This is a simple problem of rationalism.

Let us tackle this problem.

We can easily solve this problem as follows,

We know that,

To rationalize the denominator we must multiply and divide the number by the denominator's conjugate.

Now,

The Conjugate of the denominator is  √3+1.

We know that, (a+b) ( a-b) = a² - b².

So, (√3-1)(√3+1) = (√3)²-1² = 3 - 1 = 2.

So, after rationalizing, we get,

$\frac{2}{(\sqrt{3}-1)(\sqrt{3}+1) }$

= $\frac{2}{2}$

= $1$

Hence, the answer is 1.

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