4 Square Root Of 5

Square Root Calculator

Calculator Use

Apply this calculator to find the main foursquare root and roots of real numbers. Inputs for the radicand x can be positive or negative real numbers. The answer will too tell you lot if you entered a perfect square.

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

Foursquare Roots, odd and fifty-fifty:

There are two 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 = ten. Square roots is a specialized form of our mutual roots calculator.

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

Perfect Square Figurer

This computer volition also tell you if the number yous entered is a perfect square or is not a perfect foursquare.  A perfect square is a number x where the square root of ten is a number a such that a^two = x and a is an integer. For instance, iv, ix and 16 are perfect squares since their square roots, 2, 3 and iv, respectively, are integers.

Example Square Roots:

• The 2nd root of 81, or 81 radical ii, or the square root of 81 is written as $$ \sqrt[two]{81} = \sqrt[]{81} = \pm ix $$.
• The 2nd root of 25, or 25 radical ii, or the square root of 25 is written every bit $$ \sqrt[2]{25} = \sqrt[]{25} = \pm 5 $$.
• The 2d root of 100, or 100 radical 2, or the square root of 100 is written equally $$ \sqrt[2]{100} = \sqrt[]{100} = \pm x $$.
• The second root of 10, or 10 radical 2, or the square root of 10 is written as $$ \sqrt[2]{x} = \sqrt[]{10} = \pm three.162278 $$.

To calculate fractional exponents use our calculator for Fractional Exponents.

References

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

Boosted reading on square roots:

At Math is Fun: square root

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