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How to Input Square Root and Parenthesis in Calculator

Reviewed by Calculator Editorial Team

Properly inputting square roots and parentheses in calculators is essential for accurate mathematical expressions. This guide explains how to correctly format these elements in different calculator types, including scientific, graphing, and online calculators.

How to Input Square Root

The square root symbol (√) represents the number that, when multiplied by itself, gives the original number. Here's how to input it in different calculators:

Scientific Calculator

  1. Locate the square root button, often labeled with √ or "sqrt".
  2. Press the √ button.
  3. Enter the number you want to find the square root of.
  4. Press the equals (=) button to get the result.

Graphing Calculator

  1. In the home screen, press the √ button.
  2. Enter the number or expression inside the square root.
  3. Press the ENTER key to calculate.

Online Calculator

  1. Look for the √ symbol in the calculator's function buttons.
  2. Click the √ button.
  3. Enter the number or expression inside the square root.
  4. Click the equals button to see the result.

Formula: √a = b, where b × b = a

Mobile Calculator

On mobile devices, the process is similar to scientific calculators. Tap the √ button, enter the number, and tap equals.

How to Input Parentheses

Parentheses ( ) are used to group operations and change the order of calculations. Here's how to use them:

Scientific Calculator

  1. Locate the parentheses buttons, often labeled with ( and ).
  2. Press the ( button to start a group.
  3. Enter the numbers and operations inside the parentheses.
  4. Press the ) button to close the group.
  5. Complete the calculation as needed.

Graphing Calculator

  1. In the home screen, press the ( button to start a group.
  2. Enter the expression inside the parentheses.
  3. Press the ) button to close the group.
  4. Press the ENTER key to calculate.

Online Calculator

  1. Look for the ( and ) buttons in the calculator interface.
  2. Click the ( button to start a group.
  3. Enter the numbers and operations inside the parentheses.
  4. Click the ) button to close the group.
  5. Click the equals button to see the result.

Note: Parentheses can be nested to create more complex expressions.

Combining Square Roots and Parentheses

When combining square roots and parentheses, follow these guidelines:

  1. Use parentheses to clearly define the scope of the square root operation.
  2. Ensure parentheses are properly closed.
  3. For complex expressions, use multiple sets of parentheses to maintain the correct order of operations.

Example Expression

√(a + b) × (c - d)

Breakdown:

  1. Calculate the sum inside the first parentheses: a + b
  2. Find the square root of that sum: √(a + b)
  3. Calculate the difference inside the second parentheses: c - d
  4. Multiply the results: √(a + b) × (c - d)

Common Mistakes

Avoid these common errors when inputting square roots and parentheses:

  • Missing parentheses: Forgetting to close parentheses can lead to incorrect calculations.
  • Incorrect nesting: Improperly nesting parentheses can change the intended order of operations.
  • Misplacing the square root symbol: Applying the square root to only part of an expression when you meant the whole.
  • Ignoring operator precedence: Not understanding that operations inside parentheses are calculated first.

Tip: Double-check your expression before pressing equals to ensure all parentheses are properly closed and the square root symbol is correctly placed.

Example Calculations

Here are some worked examples demonstrating proper input of square roots and parentheses:

Example 1: Simple Square Root

Calculate √16

  1. Press the √ button.
  2. Enter 16.
  3. Press equals.
  4. Result: 4

Example 2: Expression with Parentheses

Calculate (5 + 3) × 2

  1. Press the ( button.
  2. Enter 5 + 3.
  3. Press the ) button.
  4. Press the × button.
  5. Enter 2.
  6. Press equals.
  7. Result: 16

Example 3: Combined Square Root and Parentheses

Calculate √(9 + 16)

  1. Press the √ button.
  2. Press the ( button.
  3. Enter 9 + 16.
  4. Press the ) button.
  5. Press equals.
  6. Result: 5

Frequently Asked Questions

What happens if I forget to close a parenthesis?

If you forget to close a parenthesis, the calculator may display an error message or calculate the expression incorrectly, as it won't know where the grouped operations end.

Can I use square roots inside parentheses?

Yes, you can use square roots inside parentheses. The square root operation will be performed first, and then the result will be used in the expression inside the parentheses.

How do I input a square root of a negative number?

Most calculators will display an error when trying to find the square root of a negative number, as square roots of negative numbers are not real numbers. For complex numbers, you may need a more advanced calculator.

Can I use parentheses without a square root?

Yes, parentheses can be used without a square root to group operations and change the order of calculations. This is useful for controlling the order of operations in complex expressions.

What if I press the square root button twice?

Pressing the square root button twice will apply the square root operation to the result of the first square root. For example, √√16 would be calculated as √4, which equals 2.