Question

Nyatakan penjumlahan dan pengurangan berikut ke bentuk akar yg paling sederhana

A.15 akar 7 - 7 akar 7
B.4 akar 147 + 3 akar 363
C.4 akar 80 - 2 akar 245 + 5 akar 180
D. 2 akar 329 + 3 akar 162 - 4 akar 98

Answer 1

A. 15√7 - 7√7 = 8√7

B. 4√147 + 3√363 
= 4√(7² . 3) + 3√(11² . 3)
= 4 . 7√3 + 3 . 11√3
= 28√3 + 33√3
= 61√3

C. 4√80 - 2√245 + 5√180
= 4√(4² . 5) - 2√(7² . 5) + 5√(6² . 5)
= 4 . 4√5 - 2 . 7√5 + 5 . 6√5
= 16√5 - 14√5 + 30√5
= 32√5


D. 2√329 + 3√162 - 4√98
= 2√329 + 3√(9² . 2) - 4√(7² . 2)
= 2√329 + 3 . 9√2 - 4 . 7√2
= 2√329 + 27√2 - 28√2
= 2√329 - √2

Answer 2

A. 15√7 - 7√7 = 8√7

B. 4√147 + 3√363 = 4√(49×3) + 3√(121×3)
= 4×7√3 + 3×11√3 = 28√3 + 33√3 = 61√3

C. 4√80 -2√245 + 5√180 = 4√(16×5) - 2√(49×5) + 5√(36×5)
= 4×4√5 - 2×7√5 + 5×6√5
= 16√5 - 14√5 + 30√5
= 32√5

D. 2√329 + 3√162 - 4√98 = 2√329 + 3√(81×2) - 4√(49×2)
= 2√329 + 3×9√2 - 4×7√2
= 2√329 + 27√2 - 28√2
= 2√329 - √2