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August 2022
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[tex]1) \frac{ \sqrt[3]{72}* \sqrt{108} }{ \sqrt[6]{192} } =............ 2) \frac{ \sqrt{96}* \sqrt[3]{36} }{ \sqrt[6]{6} } [/tex]
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m11m
1) 72=2³ * 3²
108=2² * 3³
192=2^(6) *3
∛72 * √108
=
∛(2³*3²) * √(2²*3³)
=
2 ∛3² * 2 √3³
=
(6)√192 (6)√(2^(6)*3) 2 * (6)√3
=
2 (6)√3^(4) * (6)√3^(9)
= 2 * (6)√(3^(4+9-1)) = 2 * (6)√3^(12) =
(6)√3
= 2 * 3² = 18
2) 96=2^(5) *3
36=2²*3²
6=2*3
√96 * ∛36
=
√(2^(5)*3) * ∛(2²*3²)
=
(6)√(2^(5)*3)³ * (6)√(2²*3²)²
=
(6)√6 (6)√(2*3) (6)√(2*3)
=
(6)√(2^(15) * 3³ * 2^(4) *3^(4))
= (6)√(2^(18) * 3^(6)) =
(6)√(2*3)
=2³ * 3 = 8*3=24
1 votes
Thanks 1
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Answers & Comments
108=2² * 3³
192=2^(6) *3
∛72 * √108 = ∛(2³*3²) * √(2²*3³) = 2 ∛3² * 2 √3³ =
(6)√192 (6)√(2^(6)*3) 2 * (6)√3
=2 (6)√3^(4) * (6)√3^(9) = 2 * (6)√(3^(4+9-1)) = 2 * (6)√3^(12) =
(6)√3
= 2 * 3² = 18
2) 96=2^(5) *3
36=2²*3²
6=2*3
√96 * ∛36 = √(2^(5)*3) * ∛(2²*3²) = (6)√(2^(5)*3)³ * (6)√(2²*3²)² =
(6)√6 (6)√(2*3) (6)√(2*3)
=(6)√(2^(15) * 3³ * 2^(4) *3^(4)) = (6)√(2^(18) * 3^(6)) =
(6)√(2*3)
=2³ * 3 = 8*3=24