Question

Which of the following is not irrational 
(2-√3)²

(√2 - √3) (√2 +√3)

(√2 +√3)²

​

Answer 1

Answer:

(√2 - √3) (√2 +√3)

Step-by-step explanation:

(√2 - √3) (√2 +√3) is not irrational because

= 2 - 3

= -1

Answer 2

Answer (√2 - √3) (√2 +√3) is not irrational no.

Step-by-step explanation

Given: (1) (2-√3)²

           (2) (√2 - √3) (√2 +√3)

           (3) (√2 +√3)²

To find: We have to find here which one is not an irrational.

Explanation:

Step 1: $(2-\sqrt{3})^{2} =2^{2} -2(2)(\sqrt{3} )+(\sqrt{3})^{2}$

                            $=4-4\sqrt{3} +3$

                            $=7-4\sqrt{3}$

Since remainder is not rational, therefore (2-√3)² is irrational.

Step 2: $(\sqrt{2} -\sqrt{3} ) (\sqrt{2} +\sqrt{3} )=(\sqrt{2} )^{2} -(\sqrt{3} )^{2}$

                                               $=2-3$

                                               $=-1$

Since, remainder is rational, therefore $(\sqrt{2}-\sqrt{3} ) (\sqrt{2} +\sqrt{3} )$ is not irrational.

Step 3:$(\sqrt{2} -\sqrt{3} )^{2} = (\sqrt{2} )^{2} +2(\sqrt{2} )(\sqrt{3} )+(\sqrt{3} )^{2}$

                              $=2+2\sqrt{6} +3$

                              $=5+2\sqrt{6}$

Hence, $5+2\sqrt{6}$ is not rational, therefore $(\sqrt{2} +\sqrt{3} )^{2}$ is irrational.

#SPJ2

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