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The proof is by the method of reductio ad absurdum. We start by assuming that cuberoot of 26, cbrt(26), is rational. That means that the cube root can be expressed in the form p/q where p and q are co-prime integers. That is, cbrt(26) = p/q.Therefore, p^3/q^3 = 26 which can also be expressed as 26*q^3 = p^3 Now 26 = 2*13 so 2 divides the left hand side (LHS) and therefore it must divide the right hand side (RHS). That is, 2 must divide p^3 and since 2 is a prime, 2 must divide p. That is p = 2*r for some integer r. Then substituting for p gives, 26*q^3 = (2*r)^3 = 8*r^3 Dividing both sides by 2 gives 13*q^3 = 4*r^3. But now 2 divides the RHS so it must divide the LHS. That is, 2 must divide q^3 and since 2 is a prime, 2 must divide q. But then we have 2 dividing p as well as q which contradicts the requirement that p and q are co-prime. The contradiction implies that cbrt(26) cannot be rational.
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Is the square root of 26 rational or irrational?
It is an irrational number because it can't be expressed as a fraction
What is the Square root of 3744?
It is an irrational number and it is 12 times the square root of 26
Is 6 square root of 26 rational number?
It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.
What is the cube root of 26?
To find the CUBE root , we note that 27 is 3^(3) . So '3' is the cube root of '27'. Also 8 = 2^(3) . so '2' is the cube root of '8'. So the cube root of 26 is between '2' & '3'. Since it is very close to '3' ; (by 26 & 27) they we can try 2.9^3 2.9^(3) = 24.389 (2.9 is too low) So try 2.95 2.95^(3) = 25.67.. ( Still too low) Try 2.975 2.975^(3) = 26.333 .. ( Now too high) So try 2.97 2.97^(3) = 26.198 ( Too high Try 2.968 2.968^(3) = 26.145... (Too high ; try 2.965 2.965^(3) = 26.065... (Too high : try 2.964 2.964^(3) = 26.0396 (Too high ) You keep trying like this. Until you find the root to the required number of decimal places. However on the calculator 26^(1/3) = 2.962496068....
26 rational irrational?
26 is a rational number
Is the square root of 26 a rational number or irrational number?
the square root of 26 is a irrational number
How do you find the height of a cube if the volume is 26?
It will be the cube root of 26
What is the cube root of 17576?
26
Is the square root of 26 rational or irrational?
It is an irrational number because it can't be expressed as a fraction
What is the Square root of 3744?
It is an irrational number and it is 12 times the square root of 26
Is the square root of 26 an irrational number?
Yes
Is the square root of 26 rational or irrational number?
It is an irrational number because it can't be expressed as a fraction
Is 6 square root of 26 rational number?
It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.
Is the square root of 26 irrational?
No. It is not a real number but an imaginary one.
Does 26 have a square root?
Yes but it is an irrational number that can't be expressed as a fraction
What is the cube root of 26?
To find the CUBE root , we note that 27 is 3^(3) . So '3' is the cube root of '27'. Also 8 = 2^(3) . so '2' is the cube root of '8'. So the cube root of 26 is between '2' & '3'. Since it is very close to '3' ; (by 26 & 27) they we can try 2.9^3 2.9^(3) = 24.389 (2.9 is too low) So try 2.95 2.95^(3) = 25.67.. ( Still too low) Try 2.975 2.975^(3) = 26.333 .. ( Now too high) So try 2.97 2.97^(3) = 26.198 ( Too high Try 2.968 2.968^(3) = 26.145... (Too high ; try 2.965 2.965^(3) = 26.065... (Too high : try 2.964 2.964^(3) = 26.0396 (Too high ) You keep trying like this. Until you find the root to the required number of decimal places. However on the calculator 26^(1/3) = 2.962496068....
What is the least integer whose square root is an a irrational number between 5 and 7?
26 is the least integer whose square root is an irrational number between 5 and 7. This is apparent as the square root of the previous integer (25) is a rational number and since the division method for calculating the square root produces a decimal that continues infinitely without repetition.
