The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as:
It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are:
- 2.23606 79774 99789 69640 91736 68731 27623 54406 18359 61152 57242 7089... (sequence A002163 in OEIS).
which can be rounded down to 2.236 to within 99.99% accuracy. As of April 1994, its numerical value in decimal had been computed to at least one million digits.
Read more about Square Root Of 5: Proof of Irrationality, Continued Fraction, Babylonian Method, Relation To The Golden Ratio and Fibonacci Numbers, Geometry, Trigonometry, Diophantine Approximations, Algebra, Identities of Ramanujan, See Also
Famous quotes containing the words square and/or root:
“O for a man who is a man, and, as my neighbor says, has a bone in his back which you cannot pass your hand through! Our statistics are at fault: the population has been returned too large. How many men are there to a square thousand miles in this country? Hardly one.”
—Henry David Thoreau (18171862)
“Today, supremely, it behooves us to remember that a nation shall be saved by the power that sleeps in its own bosom; or by none; shall be renewed in hope, in confidence, in strength by waters welling up from its own sweet, perennial springs. Not from above; not by patronage of its aristocrats. The flower does not bear the root, but the root the flower.”
—Woodrow Wilson (18561924)