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Re: Value of M
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06 Dec 2015, 20:53
amithyarli wrote: M = √4 + ∛4 + ∜4, then the value of M is ?
A. less than 3 B. equal to 3 C. between 3 and 4 D. equal to 4 E. greater than 4 Hi, the most important point here is that any number >1, if put to any root(100th root or 200th root) will always have a value >1.. now lets see the equation.. M = √4 + ∛4 + ∜4... we know √4=2 and both ∛4 and ∜4 will be >1.. s0 M=2+ something>1 +something>1.. or M is > than 4.. Ans E
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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06 Dec 2015, 23:38
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. If M=sqrt(4)+cuberoot(4) +sqrt(sqrt(4)) , then the value of M is: A. Less than 3 B. Equal to 3 C. Between 3 and 4 D. Equal to 4 E. Greater than 4 We know that sqrt(4)=2. Since 1^3=1 < (cuberoot(4))^3=4 < 2^3=8, 1<cuberoot(4)<2. Similarly 1^4=4 < (sqrt(sqrt(4)))^4=4 <2^4=16 implies that 1<sqrt(sqrt(4))<2. So 2+1+1<M<2+2+2. M is between 4 and 6. The answer is, therefore, E.
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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07 Dec 2015, 09:23
Quote: If M = √4 + ∛4 + ∜4, then the value of M is:
A) less than 3 B) equal to 3 C) between 3 and 4 D) equal to 4 E) greater than 4
√4√4 = 2 ∛4∛1 = 1 ∛8 = 2 So, ∛4 is BETWEEN 1 and 2. In other words, ∛4 = 1.something∜4∜1 = 1 ∜16 = 2 So, ∜ is BETWEEN 1 and 2. In other words, ∜ = 1.somethingSo, √4 + ∛4 + ∜4 = 2 + 1.something + 1.something= more than 4 = E Cheers, Brent
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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21 Dec 2016, 06:56
zz0vlb wrote: If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. Less than 3 B. Equal to 3 C. Between 3 and 4 D. Equal to 4 E. Greater than 4 \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\) Or, \(M=2+2\sqrt{2}+\sqrt{2}\) Now, \(2+2\sqrt{2} = 4.xx\) Hence, the correct answer will always be > 4 Answer will be (E) Greater than 4
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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11 Feb 2017, 21:30
Bunuel wrote: zz0vlb wrote: If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. less than 3 B. equal to 3 C. between 3 and 4 D. equal to 4 E. greater than 4 Here is a little trick: any positive integer root from a number more than 1 will be more than 1. For instance: \(\sqrt[1000]{2}>1\). Hence \(\sqrt[3]{4}>1\) and \(\sqrt[4]{4}>1\) > \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}=2+(number \ more \ then \ 1)+(number \ more \ then \ 1)>4\) Answer: E. Thank you Bunuel!
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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17 Feb 2018, 13:30
shrouded1 wrote: udaymathapati wrote: Please explain the answer. Attachment: Image2.JPG \(M=4^{1/2} + 4^{1/3} + 4^{1/4}\) Now we know that \(4^{1/2} = 2\) We also know that \(4^{1/4} = \sqrt{2} \approx 1.414 > 1\) And finally \(4^{1/3} > 4^{1/4} \Rightarrow 4^{1/3}>1\) So combining all three together \(M > 2+1+1 \Rightarrow M > 4\) How can it \(4^{1/4}\) be \(\sqrt{2}\) what function does exponent 1/4 have \(\sqrt{2}\) without 1/4 exponent equals aprox 1.414



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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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17 Feb 2018, 14:12



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If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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08 Mar 2018, 15:19
zz0vlb wrote: If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. Less than 3 B. Equal to 3 C. Between 3 and 4 D. Equal to 4 E. Greater than 4 Main idea:Approximate RHS by taking the cube root. Details: We have M= 4^ (1/3) + 4^ (1/3)+ 4^ (1/3) which is greater than 4 Hence E.
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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12 Mar 2018, 15:35
zz0vlb wrote: If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. Less than 3 B. Equal to 3 C. Between 3 and 4 D. Equal to 4 E. Greater than 4 We are given that M = √4 + ^3√4 + ^4√4. We need to determine the approximate value of M. Since √4 = 2, we need to determine the value of 2 + ^3√4 + ^4√4 Let’s determine the approximate value of ^3√4. To find this value, we need to find the perfect cube roots just below and just above the cube root of 4. ^3√1 < ^3√4 < ^3√8 1 < ^3√4 < 2 Let’s next determine the approximate value of ^4√4. To find this value, we need to find the perfect fourth roots just below and just above the fourth root of 4. ^4√1 < ^4√4 < ^4√16 1 < ^4√4 < 2 Since both ^3√4 and ^4√4 are greater than 1, so √4 + ^3√4 + ^4√4 > 2 + 1 + 1, and thus, √4 + ^3√4 + ^4√4 > 4. Answer: E
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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16 Oct 2018, 05:27
I found this method much easier. M= 4^1/2+ 4^1/3 + 4^1/4 =4^(1/2+1/3+1/4) After taking LCM of 4^ the numbers, we get =4^(36/12) =4^3 which is greater than 4. Answer is option E. Posted from my mobile device
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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16 Oct 2018, 06:23




Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the
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