Question

Find Cube Root of:
i) 216
ii) 48228544
iii) 3^15 × 4^12 × 5^33​

Answer 1

Answer:

1. 6
2. 364
3. 3^5 × 4^4 × 5^11

Step-by-step explanation:

i) 216

• Make factors of 216

$216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \\ 216 = {2}^{3} \times {3}^{3} \\ \sqrt[3]{216} = \sqrt[3]{ {2}^{3} \times {3}^{3} } \\ = 2 \times 3 \\ \sqrt[3]{216} = 6$

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ii) 48228544

• Make factors of 48228544.

$48228544 = \underline{2 \times 2 \times 2} \times \underline{2 \times 2 \times 2} \\ \underline{7 \times 7 \times 7} \times \underline{13 \times 13 \times 13} \\ = {2}^{3} \times {2}^{3} \times {7}^{3} \times {13}^{3 } \\ 48228544 = (2 \times 2 \times 7 \times 13 )^{3} \\ \sqrt[3]{48228544} = \sqrt[3]{(2 \times 2 \times 7 \times 13) ^{3} } \\ = 2 \times 2 \times 7 \times 13 \\ \sqrt[3]{48228544} = 364$

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iii) 3^15 × 4^12 × 5^33

${3}^{15} \times {4}^{12} \times {5}^{33} = {(3 {}^{5} )}^{3} \times {(4 {}^{4} )}^{3} \times {(5 {}^{11} )}^{3} \\ ( {3}^{5} \times {4}^{4} \times {5}^{11})^{3} \\ \sqrt[3]{ {3}^{15} \times {4}^{12} \times {5}^{33} } = \sqrt[3]{{(3}^{5} \times {4}^{4} \times {5}^{11})^{3}} \\ \sqrt[3]{ {3}^{15} \times {4}^{12} \times {5}^{33} } = {3}^{5} \times {4}^{4} \times {5}^{11}$

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Hope It Helps You

Answer 2

Answer:

³√216= ³√(2*2*2)*(3*3*3)=2*3=6

³√48228544=³√(2*2*2)*(2*2*2)*(7*7*7)*(13*13*13)=2*2*7*13= 364

3¹5*4¹²*5³³=(3'5)³*(4'4)³*(5¹¹)³=(3'5*4'4*5¹¹)³=³√3¹'5*4¹²*5³³=³√(3'5*4'4*5¹¹)

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