Question

69. 1)(√2+√3)²; 3) (√6-√8) ²; 2) (√7+√9 )²; 4) (√11-√12) ².​

Answer 1

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1.(√2+√3)²=√4+√9=2+3=5

2. (√7+√9)²=√49+√9²=7+9=16

3. (√6-√8)²=√36-√64=6-8=-2

4 (√11-√12)²=√121-√144=11-12=-1

Answer 2

Let's calculate the values of the given expressions:

1. (√2 + √3)²: Expanding the expression, we have: (√2 + √3)² = (√2)² + 2(√2)(√3) + (√3)² = 2 + 2√6 + 3 = 5 + 2√6

2. (√7 + √9)²: Since √9 = 3, we have: (√7 + √9)² = (√7 + 3)² = (√7)² + 2(√7)(3) + 3² = 7 + 6√7 + 9 = 16 + 6√7

3. (√6 - √8)²: Since √6 and √8 cannot be simplified further, we can proceed with the calculation: (√6 - √8)² = (√6)² - 2(√6)(√8) + (√8)² = 6 - 2√48 + 8 = 14 - 8√3

4. (√11 - √12)²: Since √11 and √12 cannot be simplified further, we can proceed with the calculation: (√11 - √12)² = (√11)² - 2(√11)(√12) + (√12)² = 11 - 2√132 + 12 = 23 - 2√33

So, the values of the given expressions are:

1. (√2 + √3)² = 5 + 2√6
2. (√7 + √9)² = 16 + 6√7
3. (√6 - √8)² = 14 - 8√3
4. (√11 - √12)² = 23 - 2√33