Operasi pada Akar

a√c + b√c = (a + b)√c

a√c - b√c = (a - b)√c

a√b × c√d = (a × b)√(c × d)

(√a)² = √a × √a = √(a²) = a

Misal c = a × b, maka √c = √(a×b) = √a√b

1. 5√2 + √2 - 3√2 = (5 + 1 - 3)√2 = 3√2

2. √3 + √27 - ⅓√81 = √3 + √(9×3) - ⅓(9)

= √3 + √9√3 - 3

= √3 + 3√3 - 3

= (1+3)√3 - 3

= 4√3 - 3

3. 3√24 - √150 + 2√54

= 3√(4×6) - √(25×6) + 2√(9×6)

= 3√4√6 - √25√6 + 2√9√6

= 3(2√6) - 5√6 + 2(3√6)

= 6√6 - 5√6 + 6√6

= (6-5+6)√6

= 7√6

4. (4√2)(3√5) = (4×3)√(2×5)

= 12√10

5. 3√2 (√2 + √3) = 3(√2)² + 3√2√3

= 3(2) + 3√(2×3)

= 6 + 3√6

6. (√2 + √12)(√18 + 3√3)

= (√2 + √(4×3))(√(9×2) + 3√3)

= (√2 + √4√3)(√9√2 + 3√3)

= (√2 + 2√3)(3√2 + 3√3)

= 3(√2)² + 3√(2×3) + 6√(3×2) + 6(√3)²

= 3(2) + 3√6 + 6√6 + 6(3)

= 6 + (3+6)√6 + 18

= 24 + 9√6

Semoga membantu.

Note:

Kalau sudah paham proses utk menghitung √c = √(a×b) = √a√b, bisa langsung cantumin hasilnya.

Misal buat nentuin √24, bisa langsung cantumkan 2√6, tidak perlu cantumkan proses √(4×6) = √4√6

Tapi jika perlu tuliskan cara lengkap, ga masalah jika ingin dicantumkan.