Question

State whether the following numbers are rational or not. explain


1. (2+√2)²
2. (3-√3)²
3. (5+√5) (5-√5)
4. (√3-√2)²
5. (3/2√2)²
6. (√7/6√2)²​

Answer 1

Answer:

Step by step explanation

(2+ root 2 )² = 2² +2(2)(root 2) +(root 2 )²

4 + 4 root 2 +2

6+ 4 root 2 = irrational

2. (3- root 3)² = 3² +( root 3)² -2(3)(root 3)

9 + 3 - 6 root 3

12- 6 root 3 = irrational

3. 5² - (root 5)²

25 - 5

20 = rational

4. (root 3 - root 2)²

( root 3)² +( root 2)² - 2(root 3) (root 2)

3 + 2 - 2 root 6

5 - 2 root 6= irrational

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