Bonjour,
(√15 + √10)² = (√15)²+2(√15)(√10)+(√10)²
= 15 + 2√150 + 10
= 25 + 2√(25×6)
= 25 + 2√(5²×6)
= 25 + 2(5)√6
= 25 + 10√6
donc : (√15 + √10)²-10√6 = 25 + 10√6 - 10√6 = 25
et √25 = 5
donc : √((√15 + √10)²-10√6) = 5
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Verified answer
Bonjour,
(√15 + √10)² = (√15)²+2(√15)(√10)+(√10)²
= 15 + 2√150 + 10
= 25 + 2√(25×6)
= 25 + 2√(5²×6)
= 25 + 2(5)√6
= 25 + 10√6
donc : (√15 + √10)²-10√6 = 25 + 10√6 - 10√6 = 25
et √25 = 5
donc : √((√15 + √10)²-10√6) = 5