mohon dibantu yah guys makasih! ^^.... Question from @Charla126

Penjelasan dengan langkah-langkah:

3).

a). √(125)^4/3 = √(5³)^4/3 = √5⁴ = 5^(4/2) = 5² = 25

b). √³√(16) . ³√(1/4) = ⁶√(16) . ³√(1/4) = ⁶√(2⁴) . ³√(1/4) = 2^(4/6) . ³√(1/4) = 2^(⅔) . ³√(1/4) = ³√2² . ³√(1/4) = ³√(2² . 1/4) = ³√(4/4) = ³√1 = 1

c). √27+2√12-√75= √(9.3) +2√(4.3) -√(25.3) = 3√3+2(2)√3 -5√3=3√3+4√3-5√3=(3+4-5)√3=2√3

4).

a). 5/√3 = 5/√3 x √3/√3 = (5√3)/3 = (5/3)√3

b). 8/(3+√2) =8/(3+√2) x (3-√2)/(3-√2) = 8(3-√2)/(3²-(√2)²) = 8(3-√2)/(9-2)= 8(3-√2)/7= 8/7(3-√2)

c). √3/(√5-√2) = √3/(√5-√2) x (√5+√2)/(√5+√2) = √3(√5+√2)/((√5)²-(√2)²) = (√15+√6)/(5-2)=(√15+√6)/3 = ⅓ (√15+√6)

1 votes Thanks 2

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Nomor 3

$\begin{aligned}\sf a. \: \sqrt{ {125}^{ \frac{4}{3} } } &=\sf \sqrt{ { {(5}^{3} )}^{ \frac{4}{3} } } \\ \sf &=\sf \sqrt{ {5}^{ \frac{12}{3} } } \\ \sf &= \sf \sqrt{ {5}^{4} } \\ \sf &=\sf {5}^{2}\\ \sf &=\sf 25 \end{aligned}$

$\begin{aligned}\sf b. \sqrt{ \sqrt[3]{16} } \: . \: \sqrt[3]{ \frac{1}{4} } &=\sf \sqrt[2 \times 3]{16} \: . \: \sqrt[3]{ \frac{1}{4} } \\ \sf &=\sf \sqrt[6]{16} \: . \: \sqrt[6]{ \left(\dfrac{1}{4} \right)^{2} } \\ \sf &= \sf \sqrt[6]{16 \times \frac{1}{16} } \\ \sf &=\sf \sqrt[6]{1}\\ \sf &=\sf 1 \end{aligned}$

$\begin{aligned}\sf c. \: \sqrt{27} + 2 \sqrt{12} - \sqrt{75} &=\sf \sqrt{9.3} + 2 \sqrt{4.3} - \sqrt{25.3} \\ \sf &=\sf \sqrt{9} \sqrt{3} + 2 \sqrt{4} \sqrt{3} - \sqrt{25} \sqrt{3} \\ \sf &= \sf 3 \sqrt{3} + 2.2 \sqrt{3} - 5 \sqrt{3} \\ \sf &=\sf 3 \sqrt{3} + 4 \sqrt{3} - 5 \sqrt{3}\\ \sf &=\sf2 \sqrt{3} \end{aligned}$

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Nomor 4

$\begin{aligned}\sf a. \: \frac{5}{ \sqrt{3} } &=\sf \frac{5}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \sf &=\sf \frac{5 \sqrt{3} }{ \sqrt{9} } \\ \sf &= \sf \frac{5 \sqrt{3} }{3} \end{aligned}$

$\begin{aligned}\sf b. \: \frac{8}{3 + \sqrt{2} } &=\sf \frac{8}{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } \\ \sf &=\sf \frac{8(3 - \sqrt{2} )}{(3 + \sqrt{2})(3 - \sqrt{2} )} \\ \sf &= \sf \frac{24 - 8 \sqrt{2} }{9 - 2} \\ \sf &=\sf \frac{24 - 8 \sqrt{2} }{7} \end{aligned}$

$\begin{aligned}\sf c. \: \frac{ \sqrt{3} }{ \sqrt{5} - \sqrt{2} } &=\sf \frac{ \sqrt{3} }{ \sqrt{5} - \sqrt{2} } \times \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } \\ \sf &=\sf \frac{ \sqrt{3} \: ( \sqrt{5} + \sqrt{2} )}{( \sqrt{5} - \sqrt{2})(5 + \sqrt{2} ) } \\ \sf &= \sf \frac{ \sqrt{15} + \sqrt{6} }{5 - 2} \\ \sf &=\sf \frac{ \sqrt{15} + \sqrt{6} }{3} \end{aligned}$

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