How to Simplify Square Roots on Ti-84 Calculator

Simplifying square roots is a fundamental math skill that helps you work with radicals more efficiently. On the TI-84 calculator, you can simplify square roots using its built-in functions. This guide will walk you through the process step-by-step.

Introduction

A square root is a value that, when multiplied by itself, gives the original number. Simplifying square roots means expressing them in the form √(a×b) where a is the largest perfect square factor of b. This makes calculations easier and helps in solving more complex problems.

On the TI-84 calculator, you can simplify square roots using the square root function (√) and the fraction function (÷). The calculator can handle both exact and decimal forms of square roots, but simplifying them to their exact form is often preferred for precision.

Basic Method for Simplifying Square Roots

To simplify a square root, follow these steps:

Factor the number under the square root into a product of perfect squares and other factors.
Separate the square root of the perfect square from the other factors.
Simplify the square root of the perfect square.

Example

Simplify √(72):

Factor 72 into 36 × 2 (since 36 is a perfect square).
Write √(36 × 2) as √36 × √2.
Simplify √36 to 6, so the simplified form is 6√2.

Using the TI-84 Calculator

Here's how to simplify square roots on your TI-84 calculator:

Press the MATH key and select 4: √(.
Enter the number you want to find the square root of.
Press ENTER to see the decimal approximation.
To simplify the square root, you'll need to factor the number manually and then use the calculator to verify the simplified form.

Tip

For exact simplified forms, it's often easier to factor the number outside the calculator and then use the calculator to verify the simplified square root.

Examples

Let's look at a few examples of simplifying square roots on the TI-84 calculator.

Original Square Root	Simplified Form	Verification on TI-84
√(50)	5√2	√(50) ≈ 7.071, 5√2 ≈ 7.071
√(80)	4√5	√(80) ≈ 8.944, 4√5 ≈ 8.944
√(108)	6√3	√(108) ≈ 10.392, 6√3 ≈ 10.392

Common Mistakes to Avoid

When simplifying square roots on the TI-84 calculator, be careful of these common mistakes:

Not factoring the number correctly. For example, 72 is 36 × 2, not 16 × 4.5.
Forgetting to simplify the perfect square. For example, √36 should be simplified to 6, not left as √36.
Using the decimal approximation as the simplified form. The simplified form should be in exact radical form.

FAQ

Can the TI-84 calculator simplify square roots automatically?: No, the TI-84 calculator does not automatically simplify square roots. You need to factor the number manually and then use the calculator to verify the simplified form.
What if the number under the square root is not a perfect square?: If the number is not a perfect square, you can still simplify it by factoring out the largest perfect square factor. For example, √(18) simplifies to 3√2.
How do I simplify square roots of fractions?: To simplify √(a/b), you can write it as √a/√b and then simplify each square root separately. For example, √(8/2) = √8/√2 = 2√2/√2 = 2.
Can I simplify square roots of negative numbers?: No, the TI-84 calculator does not handle square roots of negative numbers in real numbers. Square roots of negative numbers are considered imaginary and are represented with the letter "i".