apa kunci jawaban nya

Jawaban:@Ara14123) Sederhanakan! a. √(18) + √(72) - √(50) + √(27) - √(18) = √(9 * 2) = 3√2- √(72) = √(36 * 2) = 6√2- √(50) = √(25 * 2) = 5√2- √(27) = √(9 * 3) = 3√3- 3√2 + 6√2 - 5√2 + 3√3 = (3+6-5)√2 + 3√3 = 4√2 + 3√3 4) Hitunglah a. (2√3)^4 + 3√(64) - (2√3)^4 = 2^4 * (√3)^4 = 16 * 3^2 = 16 * 9 = 144- 3√(64) = 3 * 8 = 24- 144 + 24 = 168 b. 8 2/3 + 81 3/4 + (3√3)^(2/3) - 8 2/3 = 26/3- 81 3/4 = 327/4- (3√3)^(2/3) = (3 * 3^(1/2))^(2/3) = (3^(3/2))^(2/3) = 3^(3/2 * 2/3) = 3^1 = 3- 26/3 + 327/4 + 3 = (26 * 4 + 327 * 3 + 3 * 12) / 12 = (104 + 981 + 36) / 12 = 1121 / 12 5) Rasionalkan a. 35 / (2√7) - 35 / (2√7) = (35 / (2√7)) * (√7 / √7) = (35√7) / (2 * 7) = (35√7) / 14 = (5√7) / 2 b. (1 + √3) / (4 * 2√3) - (1 + √3) / (8√3) = ((1 + √3) / (8√3)) * (√3 / √3) = (√3 + 3) / (8 * 3) = (√3 + 3) / 24 1. (Saya asumsikan ini juga soal merasionalkan) a. (√5 + √3)(√5 - √3) - Ini adalah bentuk (a+b)(a-b) = a² - b²- (√5)^2 - (√3)^2 = 5 - 3 = 2 c. 4 / (√3 - 1) - (4 / (√3 - 1)) * ((√3 + 1) / (√3 + 1)) = (4(√3 + 1)) / (3 - 1) = (4(√3 + 1)) / 2 = 2(√3 + 1) = 2√3 + 2 d. (√2 - √3)(√2 - 5√3) - √2 * √2 - 5√2√3 - √3√2 + 5√3√3 = 2 - 5√6 - √6 + 5 * 3 = 2 - 6√6 + 15 = 17 - 6√6 e. √3(2 - 5√3) - 2√3 - 5√3√3 = 2√3 - 5 * 3 = 2√3 - 15 g. √6 / (2 - √5) - (√6 / (2 - √5)) * ((2 + √5) / (2 + √5)) = (√6(2 + √5)) / (4 - 5) = (2√6 + √30) / -1 = -2√6 - √30 h. (1 - √3) / (1 + √3) - ((1 - √3) / (1 + √3)) * ((1 - √3) / (1 - √3)) = ((1 - √3)^2) / (1 - 3) = (1 - 2√3 + 3) / -2 = (4 - 2√3) / -2 = -2 + √3 i. (6 * √3) * (5 * √12) * (3 * √15) / (15√3) - ((6√3) * (5√12) * (3√15)) / (15√3) = (6√3 * 5 * 2√3 * 3√15) / (15√3) = (6 * 5 * 2 * 3 * √3 * √3 * √15) / (15√3)- = (180 * 3 * √15) / (15√3) = (540 √15) / (15√3) = 36 √(15/3) = 36√5 j. 4√2 - 3√8 - 6√(3^2) - 5√12 - 4√2 - 3√(4 * 2) - 6 * 3 - 5√(4 * 3) = 4√2 - 3 * 2√2 - 18 - 5 * 2√3 = 4√2 - 6√2 - 18 - 10√3- = -2√2 - 18 - 10√3 Semoga membantu!

Answered by ara1412 | 2025-08-11

Penyelesaian1. [tex]\sqrt{18} + \sqrt{7^2} - \sqrt{50} + \sqrt{27}[/tex][tex](\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2})[/tex][tex](\sqrt{7^2} = \sqrt{49} = 7)[/tex][tex](\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2})[/tex][tex](\sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3})[/tex][tex]=3\sqrt{2} + 7 - 5\sqrt{2} + 3\sqrt{3}[/tex][tex](3\sqrt{2} - 5\sqrt{2}) + 7 + 3\sqrt{3} = -2\sqrt{2} + 7 + 3\sqrt{3}[/tex][tex]= 7 - 2\sqrt{2} + 3\sqrt{3}[/tex]2. a. [tex]((2\sqrt{3})^2 = 4 \cdot 3 = 12)[/tex][tex]((2\sqrt{3})^4 = (12)^2 = 144)[/tex][tex]\sqrt{64} = 8[/tex][tex]3\sqrt{64} = 3 \cdot 8[/tex][tex]= 24[/tex][tex]= 144 + 24[/tex][tex]= 168[/tex]b. [tex](8\frac{2}{3} = \frac{26}{3})[/tex][tex](81\frac{3}{4} = \frac{327}{4})[/tex][tex](3\sqrt{3} = 3^{1} \cdot 3^{1/2} = 3^{3/2})[/tex][tex]\left(3^{3/2}\right)^{2/3} = 3^{(3/2)\cdot(2/3)}[/tex][tex]= 3^{1}[/tex][tex]= 3[/tex][tex]\frac{26}{3} + \frac{327}{4} + 3[/tex][tex]\frac{26}{3} = \frac{104}{12}[/tex][tex]\frac{327}{4} = \frac{981}{12}[/tex][tex]3 = \frac{36}{12}[/tex][tex]\frac{104 + 981 + 36}{12} = \frac{1121}{12}[/tex]3. a. [tex]\frac{35}{2\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}[/tex][tex]= \frac{35\sqrt{7}}{2 \cdot 7}[/tex][tex]= \frac{5\sqrt{7}}{2}[/tex]b. [tex]\frac{1+\sqrt{3}}{8\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}[/tex][tex]= \frac{\sqrt{3} + 3}{8 \cdot 3}[/tex][tex]= \frac{\sqrt{3} + 3}{24}[/tex]

Answered by vinganzbeut | 2025-08-11