Question

The rationalization factor of 1/(2√3 - √5) is​

Answer 1

Answer:

multiply numerator and denominator by the conjugate of the irrational number, i.e., (2√3+√5)

So it becomes:

$\frac{2 \sqrt{3} + \sqrt{5} }{4 \times 3 - 5}$

$= \frac{2 \sqrt{3} + \sqrt{5} }{7}$

I hope this helps you

Answer 2

Given:

A surd 1/(2√3 - √5).

To find:

The rationalization factor of 1/(2√3 - √5).

Solution:

First of all, we need to know that the rationalization factor of a surd converts it into a rational form. It is the number that is multiplied by the surd so that it becomes rational.

So, if the surd √a + √b is in the denominator of an expression, the rationalization factor will be √a - √b.

This is because,

$(√a + √b) \times (√a - √b)$

$= a - b$, which is a rational number

So, in 1/(2√3 - √5), the rationalization factor is 2√3 + √5 as

$\frac{1 (2√3 + √5 )}{ (2√3 - √5) \times (2√3 + √5) }$

(on multiplying 2√3 + √5 on both numerator and denominator of the given expression)

$= \frac{ 2√3 + √5 }{ 12 - 5 }$

$= \frac{ 2√3 + √5 }{ 7 }$

where denominator of the given expression becomes rational.

Hence, the rationalization factor of 1/(2√3 - √5) is 2√3 + √5.