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How can you prove that the square root of two is transcendental?
Wiki User
∙ 8y ago
You can't, because it isn't. The square root of 2 is irrational, but that doesn't make it transcendental. The square root of any positive integer is ALGEBRAIC - and transcendental means "not algebraic".In this case, the square root of 2 is a root of the polynomial equation x squared - 2 = 0; therefore it is algebraic.
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoYou cannot because it is not. The square root of 2 is the solution to the polynomial equation x^2 - 2 = 0 and so it is a plain irrational number, not a transcendental.
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What is one of 2 equal factors of a number or expression?
A Square Root is one of the two equal factors of a number.
Positive numbers have two square roots a principal square root and its?
And its negative counterpart.
What is one of two equal factors of a nonnegative number called?
The square root
Can a root of a perfect square be negative?
Yes. Every perfect square has two roots: one positive and one negative.
Factor x2-2x plus 50?
That doesn't factor neatly. Applying the quadratic equation, we find two imaginary solutions: 1 plus or minus 7i times the square root of 1.x = 1 + 7ix = 1 - 7iwhere i is the square root of negative one.
What does it mean if a number is transcendental?
It means that it is not algebraic... that is, it is not the root of a polynomial expression with rational coefficients.There are infinitely more transcendental numbers than algebraic numbers, but only a few are of any practical importance... most prominently pi and e, the base of the natural logarithms.All (real) transcendental numbers are irrational, but not all irrational numbers are transcendental. For example, the square root of two is irrational, but it is not transcendental as it is a root of the equation x2 - 2 = 0, a polynomial expression with rational coefficients.
Does transcendental ean it is equal to the ratio of two integers in math?
Absolutely not. Transcendental numbers are such values as e, pi, and root 2
Square root of 2 Times Square root of 2?
The square root of two times the square root of two equals two
What is the square root of six divided by the square root of two in simplest radical form?
The square root of six divided by the square root of two equals the square root of three.
Does transcendental mean it is equal to the ratio of two integers in math?
yes * * * * * No it does not. A transcendental number is not rational. It is irrational but, further than that, it is not the root of any polynomial equation with rational coefficients.
Is it true that the square root of 2 cannot be expressed by a ratio of two integers?
yes. But I'm too lazy to show you how to prove it.
How do you simplify square root of 50 the square root of 18?
5 times the square root of two over 3 times the square root of two equals 5/3
What is the square root of the number who's square root is 2?
If this is supposed to be a riddle, it's not a very good one. The square root of the number whose square root is two is, obviously, two.
Which two square roots are used to estimate square root 67?
Square root 64 and square root 81
Which two square roots are used to estimate the square root of 43?
The square root of 36 and the square root of 49.
What is the square root of four twentyfifths?
The square root of four twenty-fifths, is two fifths, because of the fact that the square root of four is two and the square root of twenty-five is five.
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
