Why √2 is irrational?

Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!

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Is √ 2 rational or irrational and why?

Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers.

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Why are negative square roots irrational?

Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers.

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Why is √ 2 √ 2 rational?

(√2a)b=(√2)ab . Here considering a=b=√2 we get at the same result. (√2a)b=√2ab , so (√2√2)√2=√2√2√2=√22=2 is rational.

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Is 2 √ 2 rational or irrational?

2 + √2 is an irrational no.

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Proof: Square Root of 2 is Irrational

15 related questions found

Is 2 √ a rational number?

√2 is an irrational number, as it cannot be simplified.

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Can a negative square root be rational?

Square roots of negative rational numbers are not rational as the idea of the square root exists only for positive numbers.

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How do you prove something is irrational number?

How do you know a number is Irrational? The real numbers which cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0 are known as irrational numbers. For example √2 and √ 3 etc. are irrational.

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Is √ 2 a real number?

For example, 2, -3/4, 0.5, √2 are real numbers. Integers include only positive numbers, negative numbers, and zero.

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Is √ 2 a whole number?

The square root of 2 is an irrational number, meaning its decimal equivalent goes on forever, with no repeating pattern: √2=1.41421356237309...

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What is the value of ✓ 2?

The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414. This value is widely used in mathematics.

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How to prove √ 2 is irrational using method of contradiction?

1 Answer
  1. If possible Let √2 is rational.
  2. ∴ √2 = p/q, p, q ∈ z, q ≠ 0.
  3. We assume that p and q do not have any common factor.
  4. p = √2q ⇒ p = 2q2
  5. p2 is a multiple of 2 ⇒ ∴ p is a multiple of 2.
  6. ∴ p = 2k, k ∈ z ⇒ p2 = 4k.
  7. 2q2 = 4k2 ⇒ q2 = 2k2
  8. q2 = 2k2

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What type of decimal expansion of √ 2 is?

The decimal expansion of the number √2 is non – terminating non – recurring since it is an irrational number.

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Can there be a square root of zero?

The square root of 0 in the radical form is expressed as √0 and in exponent form, it is expressed as 01/2. We can't find the prime factorization of 0, since 0 is neither a prime nor a composite number. Thus, the square root of 0 is 0.

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Are negative square roots real?

Zero has one square root which is 0. Negative numbers doesn't have real square roots since a square is either positive or 0.

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Are negative roots irrational?

As √-1 is an imaginary number, it is also not a rational number. This also means the square root of any negative number is not rational.

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Is square root of negative 1 a real number?

The square root of negative 1 is not a real number. Real numbers can be represented on a number line. The square root of negative 1 cannot be represented on the number line is called an imaginary number.

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Is √ 2 √ 3 rational or irrational?

Thus, √ 2 + √ 3 is irrational.

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Is 0.0 a rational number?

Yes, zero is a rational number.

This States that 0 is a rational number because any number can be divided by 0 and equal 0. Fraction a/b shows that dividing 0 by integer results in infinity.

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Is 1 √ 2 rational or irrational?

It is not possible which means our supposition is wrong. Therefore, 1√2 cannot be rational. Hence, it is irrational.

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