Question

write the reciprocal of 2+√3

Answer 1

2-√3 is the reciprocal or rationalize of 2+√3.

Answer 2

Answer:

In mathematics, the reciprocal is simply defined as the inverse of a value or number. If n is a real numbers, then its reciprocal will be 1/n. This means we need to convert the number to its inverse form. For example, the reciprocal of 5 is 1 divided by 5, i.e. 1/5. Now, when we multiply a number by its reciprocal, it gets a value equal to 1. This is also called the multiplicative inverse.

The word reciprocal comes from the Latin words “reciprocus” which means “return”. So if we take the reciprocal of the reciprocal of the number, it will return its original value.

Find:

We find the reciprocal

Given:

reciprocal of 2+√3

Step-by-step explanation:

$x = 2 + \sqrt{3}$

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} }$

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3}$

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

Hence the reciprocal of 2+√3 is 2-√3

#SPJ3