A).
(8 + √5)²
= 8² + 2 × 8√5 + (√5)²
= 64 + 2 × 8√5 + (√5)²
= 64 + 2 × 8√5 + 5
= 64 + (2 × 8)√5 + 5
= 64 + 16√5 + 5
= 69 + 16√5
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B).
(√6 - 7)²
= (√6)² - 2√6 × 7 + 7²
= 6 - 2√6 × 7 + 7²
= 6 - 2√6 × 7 + 49
= 6 - 14√6 + 49
= 55 - 14√6
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C).
(√5 + 12)²
= (√5)² + 2√5 × 12 + 12²
= 5 + 2√5 × 12 + 12²
= 5 + 2√5 × 12 + 144
= 5 + 24√5 + 144
= 149 + 24√5
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D).
(√7 - √3)²
= (√7)² + 2√7 × √3 + (√3)²
= 7 + 2√7 × √3 + (√3)²
= 7 + 2√7 × √3 + 3
= 7 + 2 × (√7 × √3) + 3
= 7 + 2 √7 × 3 + 3
= 7 + 2√21 + 3
= 10 + 2√21
---
E).
(√2 - √6)²
= (√2)² - 2√2 × √6 + (√6)²
= 2 - 2√2 × √6 + (√6)²
= 2 - 2√2 × √6 + 6
= 2 - 2 × ( √2 × √6) + 6
= 2 - 2 √2 × 3 + 6
= 2 - 2 √12 × 6
= 2 - 2 √2² × 3 + 6
= 2 - 2 √2² × √3 + 6
= 2 - (2 × 2)√3 + 6
= 2 - 4√3 + 6
= 2 - 4√3 + 6
= 2 - 4√3
[tex] \\ \\ \tt{ \red{-Hz-}}[/tex]
a
[tex](8 + \sqrt{5} ) {}^{2} = (8 + \sqrt{5} )(8 + \sqrt{5} ) \\ = 64 + 8 \sqrt{5} + 8 \sqrt{5} + 5 \\ = 69 + 16 \sqrt{5} \\ [/tex]
b
[tex]( \sqrt{6} - 7) {}^{2} = ( \sqrt{6} - 7)( \sqrt{6} - 7) \\ = 6 - 7 \sqrt{6} - 7 \sqrt{6} + 49 \\ = 55 - 14 \sqrt{6} [/tex]
c
[tex]( \sqrt{5} + 12) {}^{2} = ( \sqrt{5} + 12)( \sqrt{5} + 12) \\ = 5 + 12 \sqrt{5} + 12 \sqrt{5} + 144 \\ = 149 + 24 \sqrt{5} [/tex]
d
[tex]( \sqrt{7} + \sqrt{3} ) {}^{2} =( \sqrt{7} + \sqrt{3} )( \sqrt{7} + \sqrt{3} ) \\ = 7 + \sqrt{21} + \sqrt{21} + 3 \\ = 10 + 2 \sqrt{21} [/tex]
e
[tex]( \sqrt{2} - \sqrt{6} ) {}^{2} = ( \sqrt{2} - \sqrt{6} )( \sqrt{2} - \sqrt{6} ) \\ = 2 - \sqrt{12} - \sqrt{12} + 6 \\ = 8 - 2 \sqrt{12} \\ = 8 - (2 \times 2 \sqrt{3} ) \\ = 8 - 4 \sqrt{3} [/tex]
[answer.2.content]
