Estimate the square root to the nearest integer calculator

When you square root a number, most of the time the results have many numbers after the decimal point.

This calculator will calculate and show you what the square root of the number you submit is to the nearest tenth (only one number after the decimal point).

To get started, please submit your square number:

Rewriting Equations and Formulas - Example 1

In mathematics, rewriting is a process of converting an expression into another expression with the same value, but with a simpler form. Rewriting is usually done by applying rules that change one expression into another, usually simpler, expression. Rewriting is used in many different fields of mathematics, but is particularly important in elementary algebra, where a number of rules for rewriting expressions are taught in school. Rewriting is also an important process in computer programming, where it is often called "simplification", "unrolling", or "unwinding".

What are Square Roots?

Definition of a square root: The opposite of squaring a number. For example, finding the square root of 81 is the same as asking, "what number, when squared, is equal to 81?"

Of course, if you know that 9 x 9 = 81, you will know that the square root of 81 is 9 (92 = 81). However, what you might not realize is that -9 is also a square root of 81, because -9 x -9 also equals 81.

In other words, all numbers greater than zero (zero can never be negative or positive) have two square roots -- one positive and one negative. This is why when using an online square root calculator, the result will always be preceded by a ± sign.

As for negative numbers, since a negative times a negative always yields a positive number, negative numbers cannot have a real value square root.

What Are Perfect Squares?

When a number has a square root that is a whole number, that number is said to be a perfect square. For example, since √4 has a square root of 2, 4 is said to be a perfect square. Here is a list of the perfect squares up to 225:

List of Perfect Squares up to 225

If you are still having a hard time understanding square roots, please let me know in the feedback form located beneath the calculator, and I will try to improve my explanations on this page.

Can I get a "root! root!"? :-)

Calculator Use

Use this calculator to find the principal square root and roots of real numbers. Inputs for the radicand x can be positive or negative real numbers. The answer will also tell you if you entered a perfect square.

The answer will show you the complex or imaginary solutions for square roots of negative real numbers.  See also the Simplify Radical Expressions Calculator to simplify radicals instead of finding fractional (decimal) answers.

Square Roots, odd and even:

There are 2 possible roots for any positive real number. A positive root and a negative root. Given a number x, the square root of x is a number a such that a2 = x. Square roots is a specialized form of our common roots calculator.

"Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)2 = (+3)2 = 9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root .......... For example, the principal square root of 9 is sqrt(9) = +3, while the other square root of 9 is -sqrt(9) = -3. In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root."[1].

Perfect Square Calculator

This calculator will also tell you if the number you entered is a perfect square or is not a perfect square.  A perfect square is a number x where the square root of x is a number a such that a2 = x and a is an integer. For example, 4, 9 and 16 are perfect squares since their square roots, 2, 3 and 4, respectively, are integers.

Example Square Roots:

• The 2nd root of 81, or 81 radical 2, or the square root of 81 is written as $$ \sqrt[2]{81} = \sqrt[]{81} = \pm 9 $$.
• The 2nd root of 25, or 25 radical 2, or the square root of 25 is written as $$ \sqrt[2]{25} = \sqrt[]{25} = \pm 5 $$.
• The 2nd root of 100, or 100 radical 2, or the square root of 100 is written as $$ \sqrt[2]{100} = \sqrt[]{100} = \pm 10 $$.
• The 2nd root of 10, or 10 radical 2, or the square root of 10 is written as $$ \sqrt[2]{10} = \sqrt[]{10} = \pm 3.162278 $$.

To calculate fractional exponents use our calculator for Fractional Exponents.

References

[1] Weisstein, Eric W. "Square Root." From MathWorld -- A Wolfram Web Resource. Square Root

Additional reading on square roots:

At Math is Fun: square root

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