Question

11. (6+5√ 3 ) - (4-3√ 3 )is :

 a rational number
 an irrational number
 a natural number
 an integer​

Answer 1

Answer:

it is an irrational number.

Step-by-step explanation:

$(6 + 5 \sqrt{3} ) - (4 - 3 \sqrt{3} ) \\ \\ = 2 + 2 \sqrt{3} \\ \\ = 2(1 + \sqrt{3} )$

Answer 2

Given,

• (6+5√ 3 ) - (4-3√ 3) is given.

To find,

• We have to find whether it is a rational, irrational, natural number, or integer.

Solution,

We can simply find whether (6+5√ 3 ) - (4-3√ 3) is a rational, irrational, natural number, or integer by solving the given expression.

                      =  (6+5√ 3 ) - (4-3√ 3)

                      = (6 +5$\sqrt{3}$ - 4 +3$\sqrt{3}$)

                    =  (2 +8$\sqrt{3}$)

An irrational number is defined as a number that has a non-terminating and non-repeating decimal expansion and cannot be expressed in the form of p/q, where q≠0.

   (2 +8$\sqrt{3}$) is an irrational number as $\sqrt{3}$ is an irrational number.

Hence,  (6+5√ 3 ) - (4-3√ 3) is (b)an irrtaional number.