Perform the indicated operations: 2√[48] + 7√[12] –√[27]?
Perform the indicated operations: 2√[48] + 7√[12] –√[27]?
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1. Find a common factor in the roots (3 in this case)
2. (2)(√3)(√16) + (7)(√3)(√4) -(√3)(√9)
3. Find roots
4. (2)(4)(√3) + (7)(2)(√3) – (3)(√3)
5. 8(√3) + 14(√3) – 3(√3)
6. Add the like terms
7.19(√3)
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memorize these rule:
√a^2 = a
√(ab) = √a * √b
2√(48) + 7√(12) – √(27)
prime factor
2 √(2 * 2 * 2 * 2 * 3) + 7√(2 * 2 * 3) – √(3 * 3 * 3)
2 √(4 * 4 * 3) + 7√(2 * 2 * 3) – √(3 * 3 * 3)
2 √( 4^2 * 3) + 7 √(2^2 * 3) – √(3^2 * 3)
use the second rule and you’ll get:
2 √(4^2) * √(3) + 7 √(2^2) * √(3) – √(3^2) * √(3)
use the first rule and you’ll get:
2 * 4 √(3) + 7 * 2 √(3) – 3 √(3)
8√(3) + 14√(3) – 3√(3)
comebine like terms
(8 + 14 – 3)√(3) = 19√(3)
so the answer: 19√(3)
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