How to Use The Square Root on Computer Calculator

Calculating square roots is a fundamental mathematical operation with applications in geometry, algebra, and many scientific fields. This guide explains how to use a computer calculator to find square roots accurately and efficiently.

How to Calculate Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 × 5 = 25.

There are several methods to calculate square roots:

Using a computer calculator (most common method)
Using the long division method (manual calculation)
Using prime factorization (for perfect squares)
Using the Newton-Raphson approximation method (advanced mathematical approach)

For most practical purposes, using a computer calculator is the fastest and most accurate method.

Using a Computer Calculator

Most computer calculators have a dedicated square root function that makes finding square roots quick and easy. Here's how to use it:

Enter the number you want to find the square root of
Press the square root button (often labeled √)
Press the equals (=) button to get the result

Note: Some calculators require you to enter the number first, then press the square root button, and finally press equals. Others may automatically display the result after pressing the square root button.

For example, to find the square root of 144:

Press the number 1, then 4, then 4
Press the √ button
Press = to see the result: 12

Square Root Formula

The square root of a number x can be represented mathematically as:

√x = y, where y × y = x

For example:

√9 = 3 (since 3 × 3 = 9)
√16 = 4 (since 4 × 4 = 16)
√2 = 1.41421356... (an irrational number)

Computer calculators use advanced algorithms to compute square roots of both perfect squares and irrational numbers with high precision.

Worked Examples

Example 1: Perfect Square

Find the square root of 100.

Enter 100 on the calculator
Press √
Press =
Result: 10

Verification: 10 × 10 = 100

Example 2: Irrational Number

Find the square root of 2.

Enter 2 on the calculator
Press √
Press =
Result: 1.4142135623730951

Verification: 1.4142135623730951 × 1.4142135623730951 ≈ 2

Example 3: Large Number

Find the square root of 1,000,000.

Enter 1,000,000 on the calculator
Press √
Press =
Result: 1000

Verification: 1000 × 1000 = 1,000,000

Frequently Asked Questions

What is the difference between square and square root?: The square of a number is obtained by multiplying the number by itself (e.g., 5² = 25). The square root is the inverse operation that finds a number which, when multiplied by itself, gives the original number (√25 = 5).
Can I find the square root of a negative number?: In real numbers, no. The square root of a negative number is not defined. However, in complex numbers, negative numbers have square roots using imaginary numbers (i).
How many decimal places does a calculator show for square roots?: Most computer calculators show about 10 decimal places for square roots. The exact number of decimal places may vary depending on the calculator model and settings.
Is the square root function available on all calculators?: Yes, the square root function is a standard feature on most scientific and graphing calculators. Basic calculators may not have this function.
Can I use the square root function for solving quadratic equations?: Yes, the square root function is essential for solving quadratic equations using the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a).