What is the value (in simplest form) of sqrt(45 + 20sqrt5) + sqrt(45 - 20sqrt5)?

0 ⤊

What is the value (in simplest form) of sqrt(45 + 20sqrt5) + sqrt(45 - 20sqrt5)?

2007-12-04 23:21:35 · 2 answers · asked by Answer Seeker 1 in Science & Mathematics ➔ Mathematics

2 answers

sqrt(45 + 20sqrt(5))
= sqrt(25 + 2*5*2*sqrt(5) + 20)
= sqrt(5² + 2*5*2*sqrt(5) + (2sqrt(5))²)
= sqrt(5 + 2sqrt(5))²
= 5 + 2sqrt(5)

Similarly:
sqrt(45 - 20sqrt(5))
= 5 - 2sqrt(5)

sqrt(45 + 20sqrt(5)) + sqrt(45 - 20sqrt(5))
= 5 + 2sqrt(5) + 5 - 2sqrt(5)
= 10

2007-12-04 23:29:46 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋

-3,819,980

2007-12-04 23:31:05 · answer #2 · answered by uj 4 · 0⤊ 1⤋