Simplify the following expressions:
(i)(√3 + √7)² (ii) (√5 - √3 )² (iii) (2√5 + 3√2)²
Answers
(i) Given : (√3 + √7)²
= (√3)² + (√7)² + 2(√3)( √7)
[By using identity , (a + b)² = a² + b² + 2ab]
= 3 + 7 + 2√21
= 10 + 2√21
(ii) Given : (√5 – √3)²
= (√5)² + (√3)² – 2(√5)(√3)
[By using identity , (a - b)² = a² + b² - 2ab]
= 5 + 3 – 2√15
= 8 – 2√15
(iii) Given : (2√5 + 3√2)²
= (2√5)² + (3√2)² + 2(2√5 )( 3√2)
[By using identity , (a + b)² = a² + b² + 2ab]
= 4 × 5 + 9 × 2 + 12√10
= 20 + 18 + 12√10
= 38 + 12√10
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Similar questions :
Simplify the following expressions :
(i) (11+√11) (11-√11)(ii) (5+√7) (5-√7)
(iii) (√8 - √2) (√8 - √2)
(iv) (3+√3) (3-√3)(v) (√5 - √2) (√5 - √2)
https://brainly.in/question/15897354
Simplify the following expressions :
(i) (4+√7) (3+√2)
(ii) (3+√3) (5 -√2)
(iii)(√5 -2) (√3-√5)
https://brainly.in/question/15897349
Formula used: (a - b)² = a² + b² - 2ab and (a + b)² = a² + b² + 2ab
Answer:
(i) (√3 + √7)²
= (√3)² + (√7)² + 2(√3)( √7)
= 3 + 7 + 2√21
= 10 + 2√21
(ii) (√5 – √3)²
= (√5)² + (√3)² – 2(√5)(√3)
= 5 + 3 – 2√15
= 8 – 2√15
(iii) (2√5 + 3√2)²
= (2√5)² + (3√2)² + 2(2√5 )( 3√2)
= 4 × 5 + 9 × 2 + 12√10
= 20 + 18 + 12√10
= 38 + 12√10