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The square root of 0 = 0.
Rational is defined as a value that can be expressed as a quotient of integers.
For example, 0/1 = 0 and 0/2 = 0. Although 0/0 is undefined, the former examples are still true. Therefore, the square root of 0 is rational.
For your knowledge, the square root of any number is rational, except for negative numbers, which are irrational. This is because two identical integers cannot be multiplied to produce a negative integer.
For instance, the square root of 25 is 5 because 5x5 = 25.
However, the square root of -25 has no real roots because neither -5x-5 nor 5x5 = -25.
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Are squares of irrational numbers always rational?
No. The cube root of 3, for example is irrational. But the square of cubert(3) is 3 to the power 2/3, which is irrational. Another example, pi2 is irrational (in fact so is pi to any non-zero power).
Can the rational zero test be used to find irrational roots as well as rational roots?
Rational zero test cannot be used to find irrational roots as well as rational roots.
How do you Represent irrational number on number line?
The same as you would a rational number. Its distance from zero will represent the number, whether it is rational or irrational.
Is 0 a rational or irrational number?
Zero (0) is a rational number, because it is a whole number and an integer.
Give the difference between rational and irrational numbers Give examples of each?
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. A rational number can be. 2 is rational. The square root of 2 is irrational.
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 nine over zero rational or irrational?
Neither. It is not defined.
Why is 3 square root of 2 is irrational?
sqrt(2) is irrational. 3 is rational. The product of an irrational and a non-zero rational is irrational. A more fundamental proof would follow the lines of the proof that sqrt(2) is irrational.
Is the square root of an irrational number rational?
No: Let r be some irrational number; as such it cannot be represented as s/t where s and t are both non-zero integers. Assume the square root of this irrational number r was rational. Then it can be represented in the form of p/q where p and q are both non-zero integers, ie √r = p/q As p is an integer, p² = p×p is also an integer, let y = p² And as q is an integer, q² = q×q is also an integer, let x = q² The number is the square of its square root, thus: (√r)² = (p/q)² = p²/q² = y/x but (√r)² = r, thus r = y/x and is a rational number. But r was chosen to be an irrational number, which is a contradiction (r cannot be both rational and irrational at the same time, so it cannot exist). Thus the square root of an irrational number cannot be rational. However, the square root of a rational number can be irrational, eg for the rational number ½ its square root (√½) is not rational.
Is the square root of 50 irrational or a rational number?
The square root of 50 is an irrational number. Irrational numbers are real numbers that cannot be expressed as a fraction a/b where a and b are integers and b is non-zero. Rational numbers are numbers that can be expressed as a fraction a/b where a and b are integers and b is not zero. The square root of 50 is approximately 7.071067812, which cannot be expressed as a fraction of integers. For example, the square root of 50 is between 7 and 71/100, but even (707110/100000)2 is approximately 50.00045521, which is still not quite 50.
Is the square root of 50 a rational or irrational?
The square root of 50 is an irrational number. Irrational Numbers are real numbers that cannot be expressed as a fraction a/b where a and b are integers and b is non-zero. Rational numbers are numbers that can be expressed as a fraction a/b where a and b are integers and b is not zero. The square root of 50 is approximately 7.071067812, which cannot be expressed as a fraction of integers. For example, the square root of 50 is between 7 and 71/100, but even (707110/100000)2 is approximately 50.00045521, which is still not quite 50.
Difference between rational and irrational?
Rational numbers can be expressed in the form p/q (where q is not equal to zero). Irrational numbers cannot be expressed in this form. For example, the square root of 2 cannot be expressed as p/q.
What happens when a rational number is divided by an irrational number?
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.
Is the square root of zero a rational number?
Yes.
Are squares of irrational numbers always rational?
No. The cube root of 3, for example is irrational. But the square of cubert(3) is 3 to the power 2/3, which is irrational. Another example, pi2 is irrational (in fact so is pi to any non-zero power).
Is the product of a rational number and an irrational number rational or irrational?
Such a product is always irrational - unless the rational number happens to be zero.
Can the sum of two irrational numbers ever be rational?
Sure. For example, the sum of:root(2) and: - root(2) is zero, which is rational.
