Comprehensive Calculator Guide
This calculator finds the square root of any non-negative number as a decimal and in simplest radical form, and tells you whether it is a perfect square. √72 is about 8.485, or 6√2 in simplest form since 72 = 36 × 2. It shows the simplification and the whole numbers the root lies between.
Square roots and simplest form
The square root of x is the number that times itself gives x. Every positive number has two square roots; √ means the positive one. Negative numbers have no real square root.
To simplify, find the largest perfect square dividing the number: √72 = √(36 × 2) = 6√2. Radicals only add when what’s inside matches.
How to Use
- Enter the number.
- Make sure it isn’t negative.
- Press “Calculate” to see the root as a decimal, in simplest form, and whether it is a perfect square.
Formula Used
√x × √x = x | √(a² × b) = a√b
Practical Examples
- Example 1: √72
- 72 = 36 × 2, so 6√2, about 8.4853, between 8 and 9.
- Example 2: √144
- A perfect square: 12.
- Example 3: √2
- Already simplest: about 1.4142.
Important Tips
- Learn the perfect squares up to 400.
- Estimate between two squares first.
- Leave exact answers in radical form.
Common Mistakes to Avoid
- Writing √(a + b) = √a + √b.
- Forgetting the negative root in x² = 25.
- Not using the largest square factor.
Frequently Asked Questions
- How do I find a square root by hand?
- Find the two squares it lies between and estimate.
- What is √72 simplified?
- 6√2.
- Do negative numbers have square roots?
- Not real ones.