How to Get The Square Root with A Calculator

Calculating square roots is a fundamental mathematical operation with applications in geometry, algebra, and many scientific fields. This guide explains how to accurately find square roots using a calculator, including step-by-step instructions, formulas, and practical examples.

How to Use a Calculator for Square Roots

Most scientific and graphing calculators have a dedicated square root function. Here's how to use it:

Turn on your calculator and clear any previous calculations.
Enter the number you want to find the square root of.
Press the square root button (often labeled with √ or √x).
Press the equals (=) button to display the result.

For example, to find the square root of 25:

Enter 25 on your calculator.
Press the √ button.
Press = to see the result: 5.

Tip: If your calculator doesn't have a dedicated square root button, you can calculate it by raising the number to the power of 0.5 (x^0.5).

Square Root Formula

The square root of a number x is a value that, when multiplied by itself, gives x. Mathematically, this is represented as:

√x = y, where y × y = x

For example:

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

Calculators use numerical methods to approximate square roots of non-perfect squares.

Worked Examples

Example 1: Perfect Square

Find √36 using a calculator:

Enter 36 on your calculator.
Press the √ button.
Press = to see the result: 6.

Verification: 6 × 6 = 36, so √36 = 6.

Example 2: Non-Perfect Square

Find √10 using a calculator:

Enter 10 on your calculator.
Press the √ button.
Press = to see the result: approximately 3.16227766.

Verification: 3.16227766 × 3.16227766 ≈ 10.

Example 3: Using Exponent Method

Find √49 using the exponent method:

Enter 49 on your calculator.
Press the ^ (exponent) button.
Enter 0.5.
Press = to see the result: 7.

Verification: 7 × 7 = 49, so √49 = 7.

Common Mistakes When Calculating Square Roots

Avoid these mistakes for accurate results:

Entering negative numbers: Square roots of negative numbers are not real numbers. Most calculators will display an error message.
Forgetting to press equals: Some calculators require you to press = after the √ button to display the result.
Confusing square and square root: Remember that squaring a number (x²) is different from finding its square root (√x).
Rounding too early: Keep more decimal places during intermediate calculations and round only at the final step.

Frequently Asked Questions

What is the difference between a square and a square root?: The square of a number is that number multiplied by itself (x² = x × x). The square root is a number that, when multiplied by itself, gives the original number (√x = y where y × y = x).
Can I find square roots of negative numbers?: In real numbers, no. Square roots of negative numbers are called imaginary numbers and use the symbol i (√-1 = i). Scientific calculators typically display an error for negative square roots.
How many decimal places should I use for square roots?: Use as many decimal places as needed for your calculation. For most practical purposes, 4-5 decimal places are sufficient. Always round the final answer appropriately for your context.
What if my calculator doesn't have a square root button?: You can calculate square roots by raising the number to the power of 0.5 (x^0.5). For example, to find √10, enter 10, press the exponent button, enter 0.5, then press equals.
How do I verify a square root calculation?: Multiply the square root by itself and check if it equals the original number. For example, if √25 = 5, then 5 × 5 should equal 25.