# what's the square root of 2?

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• 1 month ago

• 1 month ago

(1) Using the calculator, get sqr(2)~1.41421356...

(2) By the binomial expansion:

sqr(2)=

sqr(4-2)=

2(1-1/2)^(1/2)=

2[1+(-1/2)/2+((1/2)(-1/2)/2!)(-1/2)^2+((1/2)(-1/2)(-3/2)/3!)(-1/2)^3+

((1/2)(-1/2)(-3/2)(-5/2)/4!)(-1/2)^4+....]=

1.416992188 approximately;

more terms evaluated , more accurate the result.

• 1 month ago

Hi

Hatsune

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. Root 2 is an irrational number as it cannot be expressed as a fraction and has an infinite number of decimals. So, the exact value of the root of 2 cannot be determined.

thank you.

• 1 month ago

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. Root 2 is an irrational number as it cannot be expressed as a fraction and has an infinite number of decimals. So, the exact value of the root of 2 cannot be determined.

Root 2 Value

The square root of 2 is the number which when multiplied with itself gives the result as 2. It is generally represented as √2 or 2½. The numerical value of square root 2 up to 50 decimal places is as follows:

√2 = 1.41421356237309504880168872420969807856967187537694…

At present, the root 2 value is computed to 10 trillion digits. For general use, its value is truncated and is used as 1.414 to make calculations easy. The fraction 99/70 is also sometimes used as the value of √2.

• 1 month ago

The best representation would simply be:

√2

The value of that is an irrational number which means it can't be represented exactly as a fraction using integers or as a decimal that terminates or ends in a repeating pattern.

The best we can give you is a rational approximation to some number of decimal places, but that's still not exactly equal to √2.

√2 ≈ 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360...

• 1 month ago

It's the number, when multiplied by itself, gives you 2.

• ?
Lv 7
1 month ago

It's one plus a fraction.

• GA41
Lv 7
1 month ago

1.4142135623730950488016887242097

If you press the windows icon at the lower right hand corner of the page, you will get a dialog box that list  programs on your computer.  Select the calculator.  Press the list icon in the upper left corner of the calculator.  You will get a dialog box of various calculators to select.  Select the scientific calculator.  This calculator has a square root function.  If you enter the number 2 in the calculator, and press the square root function, it will give you the square root of 2..

• Marty
Lv 4
1 month ago

The square root of 2 is an irrational number, so it can't be represented in a finite sequence of digits.

When it's rounded off, it's approximately 1.414.

the square route of 2 will carry on forever, but the longest people have found is: 1.41421356237