**Math Calculators** ▶ Square Root Calculator

An online square root calculator helps you to find the square & nth root of any positive number you want. Also, this sqrt calculator tells you the number you enter is a perfect square or is not a perfect square. For example; 4, 9 & 16 are the perfect squares of 2, 3 & 4 respectively. The square root of number is the number that when multiplied by itself equal to the original number. For example the sqrt of 9 & 16 is 3& 4 respectively. If you are worrying about basic manual calculation, then keep reading to know the square root formula, calculation for fraction, negative numbers & much more!

Also, you can try our online exponent calculator that helps you to calculate the value of any number raised to any power.

But let’s ahead to some basics!

Swipe on!

To prepare for the calculation of square root, then you should remember the basic perfect square root. As the sqrt of 1, 4, 9, 16, 25, 100 is 1, 2, 3, 4, 5, and 10.

To find the sqrt of √25, let’s see!

√25 = √5*5

√25 = √5^{2}

√25 = 5

These are the simplest square roots because they give every time an integer, but what when a number have not a perfect square root? For example, you have to estimate the sqrt of 54?

- As you know √49 = 7 & √64 = 8. So, the √54 is between the 8 and 7.
- The number 54 is closer to the 49 than 64. So, you can try guessing √54 = 7.45
- Then, by squaring 7.45, 7.45
^{2}= 55.5 which is greater than 54. So you should try the smaller number. Let’s take 7.3 - By taking the square of 7.3, it gives 53.29 which is close to 54.
- It means the square root of 54 is between the 7.3 & 7.4.

Let’s take another example:

**Example:**

What is a square root of 27?

**Solution:**

As the 27 is not the perfect square of any number. So, we have to simplify it as:

√27 = √9*3

√9*√3 = 3√3

Our square root calculator considers these formulas & simplification techniques to solve the sqrt of any number or any fraction.

The sqrt of fractions can be determined by the division operation. Look at the following example:

(a/b)^1/2 = √a / √b = √a/b

Where a/b is any fraction. Let’s have another example:

**Example:**

What is square root of 9/25?

**Solution:**

√9/25 = √9 / √25

√9 / √25 = 3 / 5 = 0.6

At school level, we have been taught that the square root of negative numbers cannot exist. But, the mathematicians introduce the general set of numbers (Complex numbers). As,

x = a + bi

Where, a is real number & b is an imaginary part. The iota (i) is a complex number with a value:

i = √-1 . Let’s have some examples:

The sqrt of -4 = √-4 = √-1 * 9 = √ (-1) √9 = 3i

What is the square root of -17 = √-17 = √-1 * 17 = √ (-1) √17 = 17i

Finding square root become very easy with this roots calculator. You just have to follow the given steps for the exact calculations.

Read on!

**Inputs:**

- First of all, hit the tab to choose the square root or nth root for any number.
- Very next, enter the number for which you want to do the calculation according to the selected option.
- Lastly, click on calculate button.

**Outputs:**

Once you done, the calculator shows:

- Square root of the number.
- Nth root of the number.
- Step-by-Step calculation.

**Note:**

No matter, what the input parameter is, the online square roots calculator shows you the accurate results according to the selected input.

Yes, the positive numbers have more than one sqrt, one is positive & the other is negative.

No, it is an irrational number.

Reason:

The square root of 2 cannot be expressed as the quotient of two numbers.

Some roots are rational while others are irrational.

Square roots are frequently appearing in the mathematical formulas including quadratic formula, discriminant as well as in many physics laws. Further, it is used in many places in the daily life, used by engineers, carpenters construction managers, medical assistants and many others. When it comes to calculations for the large number, it is very tricky & complex. Simply, try the online square root calculator that helps you to determine the square root according to your need.

From the source of Wikipedia : Definition, uses & properties

From the site of virtualnerd : Square root of fractions

From the source of khanacademy : Square root of negative numbers

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