Square root of 821

If you are looking to answer the following questions: “what is the square root of 821?” The answer is 28.653097563789. 

ANSWER: square root of 821=28.653097563789

The square root of a number (821 in this case) is a number (28.653097563789 in this case) which multiplied by itself equals the number from which you are calculating the square root (821). Mathematically square root of 821 can expressed in the radical form or an exponent form as shown below:

• Radical form of the square root of 821: √821
• Exponent form of the square root of 821: (821)^½ or (821)^0.5

This symbol √ is called radical sign or radix. The number whose square root is being calculated is called the radicand. The radicand is the number underneath the radical sign (radix), in this case it is 821.

Square root of 821 calculator

If you would like to confirm the answer to the question of “what is the square root of 821?” or calculate a square root of any other number use the square root calculator:

Square root of 821 calculation guide

In the following sections we explain how to calculate the square root of 821. We will answer such common questions as: “is the square root of 821 rational or irrational?” and “is 821 a perfect square?” We will discuss what the principal square root of 821 is.  For your reference we also included the following tables:

• N^th roots of 821
• Perfect square numbers
• Square roots of numbers around 821 

You will find all the information you need on the square root of 821 calculations below. 

What is the square root of 821?

The square root of 821 is a number which multiplied by itself equals 821. Therefore, the square root of 821 is 28.653097563789 and we write it √821=28.653097563789 because 28.6530975637892=821. Since 28.6530975637892 is the same as 28.653097563789 x 28.653097563789 the following expressions is true:

821 = 28.6530975637892=28.653097563789×28.653097563789

Therefore

ANSWER: square root of 821=√821=28.653097563789

Is 821 a Perfect Square?

A number is considered a perfect square if it is a product of squaring a whole number (called integer). 0, 1, 2, 3, 4, 7, 8, and 9 are all whole numbers (same as integers). Numbers such as -8, 7.025, or 5 ½ are not whole numbers. Remember squaring is when a number is multiplied by itself. For example, 81 is a perfect square because it is a product of 92 which is the same as 9×9. Notice 9 is a whole number (integer).

In our example the square root of 821 is 28.653097563789. Since 28.653097563789 is not a whole number therefore 821 is not a perfect square.

ANSWER: 821 is not a whole number 

Is the square root of 821 rational or irrational number?

A number is rational when it can be made by dividing a whole number by a whole number. A whole number which is also called an integer does not have a fractional part itself. Simply said a number is rational if it can be written as a fraction. 

A quick method to determine if 821 is a perfect square. The square roots of perfect squares are all rational numbers. The square roots of numbers that are not a perfect square are all irrational numbers. Since we know that 821 is not a perfect square therefore 821 is not a rational number.

Principal square root of 821

Every positive number has two square roots. One of the square roots is positive and another one is negative. For example the square roots of 821 are -28.653097563789 (negative) and +28.653097563789 (positive) because  (-28.653097563789)^2=(+28.653097563789)^2=821. The positive square root is denoted as “the principal square root”. Typically, when we are calculating “the square root of a number” we mean the principal square root. In our case it is positive 28.653097563789 or +28.653097563789 which is written as 28.653097563789. As you may know if there is no minus (-) sign before a number it is a positive number. 

Again the principal square root of 821 is 28.653097563789.

Calculating the square root of 821 with a calculator

In order to calculate the square root of 821 with a basic or a scientific calculator you need to enter 821 and then press the key with this sign  “√x”

√821 = 28.653097563789

Calculating the square root of 821 in Excel and Google Sheets

There are two functions you can use to do this calculation. You can use the function SQRT () to calculate the square root of any number in Excel and Google Sheets. Click on a cell and type =SQRT(821). Hit enter. You will get 28.653097563789.

You can also use the POWER function which works like an exponent is an equation. To find a square root of 821 type =POWER (821, 1/2). Remember square roots can be expressed as exponents as we discussed earlier in this article.

Table: N^th roots of 821

In the section above we explained how the square root (which is the 2^nd root) of 821 is calculated. However there are more roots of 821. Find the N^th roots of 821 in the table below:

Table: Square root of numbers around 821

This table lists numbers around 821 and their respective square roots.

Table: Perfect square numbers

This table lists perfect square numbers from 1 through 10,000.

Visit squarerootof.net for any square root related calculations including square roots, negative square roots, square roots from fractions, exponentiation and other related calculations.