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Proof by contradiction: suppose that root 7 (I'll write sqrt(7)) is a rational number, then we can write sqrt(7)=a/b where a and b are integers in their lowest form (ie they are fully cancelled). Then square both sides, you get 7=(a^2)/(b^2) rearranging gives (a^2)=7(b^2). Now consider the prime factors of a and b. Their squares have an even number of prime factors (eg. every prime factor of a is there twice in a squared). So a^2 and b^2 have an even number of prime factors. But 7(b^2) then has an odd number of prime factors. But a^2 can't have an odd and an even number of prime factors by unique factorisation. Contradiction X So root 7 is irrational.
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Can multiplying two irrational numbers give you an irrational number?
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
Can you give one example for surd which is not irrational?
It is impossible to have a surd that is not irrational. Surds are defined to be an irrational number (square root of a number).
What systems does the square root of 5 belong?
Square root of 5 is a real number, to start with. It is irrational, also. And there are two values which, when squared, give 5 as the answer.Since they are irrational, we can give approximations: +2.236068 and -2.236068
Can an irrational number be a decimal if so give an example?
Irrational numbers are decimal numbers that can't be expressed as fractions. An example is the square root of 2
Give an example of irrational number?
pi square root of 2 e square root of 3
Give a proof that the square root of 3 is an irrational nu?
It is a prime number that has only factors of itself and one therefore it is an irrational number like all prime numbers are.
Can multiplying two irrational numbers give you an irrational number?
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
Can you give one example for surd which is not irrational?
It is impossible to have a surd that is not irrational. Surds are defined to be an irrational number (square root of a number).
Give a proof that the square root of 8 is an irrational number?
sqrt(8) = sqrt(4*2) = 2*sqrt(2).Even without given that sqrt(2) is a rational, you can give that the square root of 2 starts converging onto the "Pythagoras Constant" eventually, as it takes an infinite amount of digits to square root an integer that is not perfectly squared.Thus, an rational x irrational = irrational, thus the sqrt(8) is irrational (an approximation is 2.8284271247...).
Can you add an irrational number and a rational number to give an irrational?
No, but you can add an irrational number and a rational number to give an irrational.For example, 1 + pi is irrational.
What systems does the square root of 5 belong?
Square root of 5 is a real number, to start with. It is irrational, also. And there are two values which, when squared, give 5 as the answer.Since they are irrational, we can give approximations: +2.236068 and -2.236068
Are the square roots of all positive integers are irrational?
It might seems like it, but actually no. Proof: sqrt(0) = 0 (0 is an integer, not a irrational number) sqrt(1) = 1 (1 is an integer, not irrational) sqrt(2) = irrational sqrt(3) = irrational sqrt(4) = 2 (integer) As you can see, there are more than 1 square root of a positive integer that yields an integer, not a irrational. While most of the sqrts give irrational numbers as answers, perfect squares will always give you an integer result. Note: 0 is not a positive integer. 0 is neither positive nor negative.
Can an irrational number be a decimal if so give an example?
Irrational numbers are decimal numbers that can't be expressed as fractions. An example is the square root of 2
Are the square roots of all positive integers irrational If not give an example of the square root of a number that is a rational number?
The square root of any positive square number is always rational as for example the square root of 36 is 6 which is a rational number.
Which of the number will produce an irrational number when multiplied by 0.5?
Any irrational number, when multiplied by 0.5 will give an irrational number.
Which number produces an irrational number when added to 0.4?
Any irrational number, added to 0.4 will give an irrational number.
Does dividing an rational number by an irrational number give you an irrational number?
Yes normally it does
