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The square root of 2 is irrational because it cannot be expressed as a fraction in which the numerator and denominator are both integers.
Another way of saying this is that the square root of 2 will have infinite decimal places in any a number system of any radix (base 10, base 2, base 3, base 16, etc)
This should not be confused with imaginary numbers. Rational and Irrational Numbers together combine to make the Real numbers, imaginary numbers are, however, not Real. Imaginary numbers are those that can be expressed as a Real number multiplied by the square root of negative 1 (also known as i or j)
So, strictly speaking, both sqrt(2) and sqrt(-1) are "not rational numbers", however, they are not both "irrational" numbers.
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Is 0.692 rational or irrational?
ANY number with a finite number of decimal digits is RATIONAL.(Also, numbers with an infinite number of decimals may be rational - in which case the digits repeat - or irrational.)
How can you do squares and square roots?
A number is squared by multiplying it by itself, for example 8 is the square of 64 (8 x 8 = 64). Square roots are found by figuring out which number, when squared, will give the number in question, for example the square root of 64 is 8 (64 / 8 = 8).
How can you prove that 3 plus 2x⁵ is an irrational number where x⁵ is irrational?
1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
Give one example for if you add two irrational number and answer should get in rational number?
Suppose A = 2 + sqrt(3) and B = 5 - sqrt(3) Then A and B are two irrational numbers but A + B = 2 + sqrt(3) + 5 - sqrt(3) = 7 which is rational.
How do you find a rational number between two given rational numbers?
Add them together and divide by 2 will give one of the rational numbers between two given rational numbers.
