Prove that if (n) is any positive integer, then (sqrt{n}+sqrt{2}) is irrational.

Question:

Prove that if $n$ is any positive integer, then $\sqrt{n}+\sqrt{2}$ is irrational.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A Concise Introduction To Pure Mathematics

ISBN: 9781498722926

4th Edition

Authors: Martin Liebeck

See More Books

Question Posted: May 19, 2024 02:06 AM

See More Questions

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...
Jason borrows $ 10300 for the next 4 years at a variable interest rate. Assume that the interest accumulates for 4 years at an annual nominal rate of 11% compounded quarterly. Calculate the...
Characterize the nature of motivation, including its importance and focus Identify and describe the need theories on motivation. Identify and describe the behavior theories on motivation. Identify...
PMOs should help to ensure that organizations use the resources in the best way. This contributes to: Group of answer choices Effective use or organizations and alignment Effectiveness, efficiency,...
Aerobic organisms transfer electrons from reduced fuel molecules to O2, forming H2O. Some anaerobic organisms use nitrate (NO3-) as an acceptor for electrons from reduced fuel molecules. Use the...
If the valuation allowance had been the same in Year 3 as it was in Year 2, the company would have reported $115 h igher: A . net income. B . deferred tax assets. C . income tax expense.
Dale Reynolds has the following details from his accounts for the year ended 31 December 2012. Required: Draw up Dale Reynolds trading account for the year ended 31 December 2012. Opening inventory...
Accelerated Depreciation Koffmans Warehouse purchased a forklift on January 1, 2010, for $6,000. The forklift is expected to last for five years and have a residual value of $600. Koffmans uses the...
According to the 2016 Australian Bureau of Statistics (ABS) census what percentage of older people in Australia were born overseas? 14% 83% 5% 37% 56%
Find $n$, given that both $n$ and $\sqrt{n-2}+\sqrt{n+2}$ are positive integers.
(a) Let $a, b$ be rationals and $x$ irrational. Show that if $\frac{x+a}{x+b}$ is rational, then $a=b$. (b) Let $x, y$ be rationals such that $\frac{x^{2}+x+\sqrt{2}}{y^{2}+y+\sqrt{2}}$...
Outline the supply-side view of fiscal policy. How does this view differ from the various demand-side theories? Would a supply-side economist be more likely to favor a $1,000 rebate to all taxpayers...
Miller Companys contribution format income statement for the most recent month is shown below: Total Per Unit Sales (43,000 units) $ 344,000 $ 8.00 Variable expenses 215,000 5.00 Contribution margin...
Sound pressure level 1 m away from the source is measured to be 9 1 dB . Source is placed on a concrete floor. Calculate the theoretical sound pressure level at a distance 2 0 m from the source?...
Three different devices are producing sound at pressure levels 9 4 , 8 0 and 8 1 dB ( levels given for each device individually at same measurement location ) . Calculate the total sound pressure...
Maphefo Anno-Frempong, CEO of the Transport Education and Training Authority (TETA), one of the 21 Sector Education and Training Authorities, is assigned the responsibility of facilitating skills...
Laine Ltd. is a Canadian-controlled private corporation. Its non-eligible refundable dividend tax on hand (NERDTOH) account at December 31, 2021 was $35,000. For its 2022 taxation year, its...
A certain natural product having [a] D+ 40.3 was isolated. Two structures have been independently proposed for this compound. Which one do you think is more likely to be correct? Why?
In Problems 1522, find the principal needed now to get each amount; that is, find the present value. To get $750 after 2 years at 2.5% compounded quarterly.
The demand for freight transportation is said to be inelastic, explain
En Ramasamy and Puan Kamani are trying to figure out their current financial health. They have listed the following items from their most recent statements. They will pay off their car loan in three...
1)Highlight the Logistics Strategy Triangle 2)Highlight Postponement Characteristics 3)Highlight the importance of Contract Manufacturer in SCM 4)Explain Activity Based Costing in cost identification...

Prove that if (n) is any positive integer, then (sqrt{n}+sqrt{2}) is irrational.

Question:

Step by Step Answer:

A Concise Introduction To Pure Mathematics

Students also viewed these Mathematics questions