Square Root Greater Than 3 on Calculator Ti84
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Reviewed by Calculator Editorial Team
Finding square roots greater than 3 on the TI-84 calculator is a common math task. This guide explains how to perform this calculation accurately and understand the results.
How to Find Square Roots on TI-84
The TI-84 calculator provides several methods to find square roots. The most common approach uses the square root function (√x) in the math menu.
Step-by-Step Instructions
- Press the MATH button on your TI-84 calculator.
- Use the arrow keys to move to the NUM menu.
- Select the √x function (usually the first option).
- Enter the number you want to find the square root of.
- Press ENTER to see the result.
Note: The TI-84 can only find real square roots (non-negative results). For complex numbers, you'll need to use the complex math functions.
Finding Square Roots Greater Than 3
To find square roots greater than 3, you'll need to solve equations of the form √x > 3. Here's how to approach this:
√x > 3
Square both sides: x > 9
This means any number greater than 9 will have a square root greater than 3. For example:
- √10 ≈ 3.162 (greater than 3)
- √16 = 4 (greater than 3)
- √9 = 3 (equal to 3, not greater)
Using the TI-84 to Verify
You can use the calculator to verify these results:
- Calculate √9 to confirm it equals 3.
- Calculate √10 to see it's approximately 3.162.
- Calculate √16 to confirm it equals 4.
Worked Examples
Example 1: Find all x where √x > 3
Solution: As shown above, x must be greater than 9. So x > 9.
Example 2: Find the smallest integer where √x > 3
Solution: The smallest integer greater than 9 is 10. √10 ≈ 3.162 > 3.
| Number (x) | Square Root (√x) | Is √x > 3? |
|---|---|---|
| 9 | 3 | No |
| 10 | 3.162 | Yes |
| 16 | 4 | Yes |
| 25 | 5 | Yes |
Frequently Asked Questions
Can the TI-84 find square roots of negative numbers?
No, the TI-84 can only find real square roots. For negative numbers, you'll need to use complex number functions.
How accurate are the square roots on the TI-84?
The TI-84 provides square roots with about 10 decimal places of accuracy, which is sufficient for most educational purposes.
What if I get an ERROR when calculating square roots?
This typically happens when you try to find the square root of a negative number. Make sure your input is non-negative.