simplify the following expressions:
1.(5+√7)(2+√5)
2.(5+√5)(5-√5)
3.(√3+√7)2
4.(√11-√7)(√11+√7)
answer to this question
Answers
Simplify the following expressions:
1) (5+√7) (2+√5)
→ 5(2) + 5(√5) + √7(2) + √7(√5)
→ 10 + 5√5 + 2√7 + √35
{\underline{\boxed{\sf{10 + 5\sqrt{5} + 2\sqrt{7} + \sqrt{35}}}}}
10+5
5
+2
7
+
35
Henceforth, simplified!
3) (√3+√7)²
→ (a+b)² = a² + 2ab + b²
→ (√3+√7)² = (√3)² + 2(√3)(√7) + (√7)²
→ (√3+√7)² = 3 + 2(√21) + 7
→ (√3+√7)² = 3 + 2√21 + 7
→ (√3+√7)² = 10 + 2√21
{\underline{\boxed{\sf{10 + 2\sqrt{21}}}}}
10+2
21
Henceforth, simplified!
2) (5+√5) (5-√5)
→ (a+b)(a-b) = a² - b²
→ (5+√5) (5-√5) = (5)² - (√5)²
→ (5+√5) (5-√5) = 25 - 5
→ (5+√5) (5-√5) = 20
{\underline{\boxed{\sf{20}}}}
20
Henceforth, simplified!
4) (√11-√7)(√11+√7)
→ (a+b)(a-b) = a² - b²
→ (a-b)(a+b) = a² - b²
→ (√11-√7)(√11+√7) = (√11)² - (√7)²
→ (√11-√7)(√11+√7) = 11 - 7
→ (√11-√7)(√11+√7) = 4
{\underline{\boxed{\sf{4}}}}
4
Henceforth, simplified!