If a rectangle has a width of 5 meters and a perimeter of 50 meters calculate the area.
2 answers:
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These are 10 questions and 10 answers
1)![\sqrt[3]{24} . \sqrt[3]{45}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B24%7D%20%20.%20%5Csqrt%5B3%5D%7B45%7D%20)
Answer: third option 6∛5
Explanation:
24 = 2^3 * 3
45 = 3^2 * 5
=> 24 * 45 = 2^3 * 3^3 * 5
=> (∛24).(∛45) = ∛[ (2^3).(3^3).5 ] = (2)(3)∛5 = 6∛5
2)![\sqrt[5]{4x^2} . \sqrt[5]{4x^2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20.%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20)
Answer: second option.
Demostration:
![\sqrt[5]{4x^2} . \sqrt[5]{4x^2} = \sqrt[5]{4^2x^4} = \sqrt[5]{2^4x^4} = \sqrt[5]{16x^2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20.%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20%3D%20%20%5Csqrt%5B5%5D%7B4%5E2x%5E4%7D%20%3D%20%5Csqrt%5B5%5D%7B2%5E4x%5E4%7D%20%3D%20%5Csqrt%5B5%5D%7B16x%5E2%7D%20)
3)
Answer: first option 10
Justification:
√10 . √10 = (√10)^2 = √(10^2) = √100 = 10
4)![\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20)
Answer: fourth option: 7
Explanation:
![\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7}= (\sqrt[4]{7^})^4= \sqrt[4]{7^4}=7 ^{4/4}=7^1=7](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%3D%20%28%5Csqrt%5B4%5D%7B7%5E%7D%29%5E4%3D%20%5Csqrt%5B4%5D%7B7%5E4%7D%3D7%20%5E%7B4%2F4%7D%3D7%5E1%3D7)
5)
Answer: the third option: 7x^2 - 12x√14 + 72
Solution:
Notice that it is the two factors are identical, so this is a perfect square binomial:
(x√7 - 3√8)^2 = (x√7)^2 - 2*(x√7)(3√8) + (3√8)^2 = 7x^2 - 6√(56)x + 72 =
= 7x^2 -(6)(2)x√14 + 72 = 7x^2 - 12x√14 + 72
6) √12 . √18
Answer: the fourth option 6√6
Explanation:
√12 . √18 = √ (2 . 2 . 3 . 2 . 3 . 3) = √ [( 2^3) . (3^3)] = 2 . 3 √6 = 6√6
7)
Answer: first option y^3
Justification:
8) ∛d . ∛d . ∛d
Answer: first option: d
Explanation:
∛d . ∛d . ∛d =![( \sqrt[3]{d}) ^3 = d{3/3}=d^1=d](https://tex.z-dn.net/?f=%28%20%5Csqrt%5B3%5D%7Bd%7D%29%20%5E3%20%3D%20d%7B3%2F3%7D%3Dd%5E1%3Dd)
9)
Answer: second option
Explanation:
10) (∛4) . √3
Answer: third option![\sqrt[6]{432}](https://tex.z-dn.net/?f=%20%5Csqrt%5B6%5D%7B432%7D%20)
Explanation:
![\sqrt[3]{4} . \sqrt{3} = \sqrt[6]{4^2} . \sqrt[6]{3^3} = \sqrt[6]{16.27} = \sqrt[6]{432}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B4%7D%20.%20%5Csqrt%7B3%7D%20%3D%20%5Csqrt%5B6%5D%7B4%5E2%7D%20.%20%5Csqrt%5B6%5D%7B3%5E3%7D%20%3D%20%5Csqrt%5B6%5D%7B16.27%7D%20%3D%20%5Csqrt%5B6%5D%7B432%7D%20)
1)
Answer: third option 6∛5
Explanation:
24 = 2^3 * 3
45 = 3^2 * 5
=> 24 * 45 = 2^3 * 3^3 * 5
=> (∛24).(∛45) = ∛[ (2^3).(3^3).5 ] = (2)(3)∛5 = 6∛5
2)
Answer: second option.
Demostration:
3)
Answer: first option 10
Justification:
√10 . √10 = (√10)^2 = √(10^2) = √100 = 10
4)
Answer: fourth option: 7
Explanation:
5)
Answer: the third option: 7x^2 - 12x√14 + 72
Solution:
Notice that it is the two factors are identical, so this is a perfect square binomial:
(x√7 - 3√8)^2 = (x√7)^2 - 2*(x√7)(3√8) + (3√8)^2 = 7x^2 - 6√(56)x + 72 =
= 7x^2 -(6)(2)x√14 + 72 = 7x^2 - 12x√14 + 72
6) √12 . √18
Answer: the fourth option 6√6
Explanation:
√12 . √18 = √ (2 . 2 . 3 . 2 . 3 . 3) = √ [( 2^3) . (3^3)] = 2 . 3 √6 = 6√6
7)
Answer: first option y^3
Justification:
8) ∛d . ∛d . ∛d
Answer: first option: d
Explanation:
∛d . ∛d . ∛d =
9)
Answer: second option
Explanation:
10) (∛4) . √3
Answer: third option
Explanation: