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Number

Square root

A square root calculator will calculate the square root of any number. Note that the calculator will only take the square root of a positive number since the square root of a negative number yields an imaginary result. Before taking the square root we need to know what a square root is and how to find a square root.

A square root of a number is a number raised to the exponent of 1/2. The result is a number when multiplied by itself (squared) yields the original number. For example, the square root of 16 is 4 since 4 times 4 is 16. Note that the square root is also negative, but for many practical purposes we use only the positive value. Numbers whose square roots are whole numbers are known as *perfect squares*.

For numbers that are not perfect squares, here is a method to represent the square root of a whole number as a number multiplied by another square root.

- Write the number and determine how to find square root.
- Break down the number into factors, one of which is a perfect square.
- Simplify the factor that is a perfect square.
- Rewrite with the whole number multiplied by the square root of the prime factor.
- If you cannot find a factor that is a perfect square, then the square root cannot be simplified.
- If you want an exact value for the square root, use the square root calculator.

For example:

`√20 =√4 *√5`

`√20 = 2 *√5`

The square root calculator will give the value of `√20`

to four significant figures. The sig fig calculator will calculate this result to as many significant figures as is desired in the problem. You can check your results by using the exponent calculator which will raise any numbers to a specified exponent. This calculator is particularly handy for decimals or larger numbers raised to higher exponents.

In some applications of the square root, particularly those pertaining to sciences such as chemistry and physics, the results are preferred in scientific notation. In brief, an answer in scientific notation must have the decimal between the first two non-zero numbers and will be represented as the decimal multiplied by 10 raised to an exponent. For example, the number `0.00345`

is written as `3.45 * 10⁻³`

in scientific notation, whereas `145.67`

is written as `1.4567 * 10²`

in scientific notation. The results obtained using the square root calculator can be converted in scientific notation with the scientific notation calculator.

One can also estimate the value of a square root by determining what two numbers it must fall. This is accomplished by knowing the perfect squares. For example, suppose you want an approximate value of `√38`

. Knowing that `36`

and `49`

are perfect squares tells you that the value is between `6`

and `7`

. Since `38`

is much closer to `36`

than `49`

, we know the approximate value is slightly more than `6`

, perhaps `6.2`

. The square root calculator gives an accurate value of `6.164`

to four significant figures.