Square Root Calculator

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Square Root Calculator
Square Root (√x)Cube Root (∛x)nth Root (ⁿ√x)
Answer:
Please enter values above
function toggleInputs(){var type=document.getElementById('calc_type').value;var nthRow=document.getElementById('nth_row');if(type==='nth'){nthRow.style.display='table-row';}else{nthRow.style.display='none';}}function resetCalc(){document.getElementById('nth_row').style.display='none';document.getElementById('finalResult').innerHTML='Please enter values above';document.getElementById('stepsOutput').innerHTML=";}function calculateResult(){var x=parseFloat(document.getElementById('input_x').value);var prec=parseInt(document.getElementById('precision').value);var type=document.getElementById('calc_type').value;var showSteps=document.getElementById('showSteps').checked;var result=0;var n=2;var stepsText="";if(isNaN(x)){alert('Please enter a valid number for x');return;}if(isNaN(prec)){prec=5;}if(type==='sqrt'){n=2;if(x<0){document.getElementById('finalResult').innerHTML="Result = "+Math.sqrt(Math.abs(x)).toFixed(prec)+" i (Complex Number)";}else{result=Math.sqrt(x);document.getElementById('finalResult').innerHTML="√"+x+" = "+result.toFixed(prec);}}else if(type==='cbrt'){n=3;result=Math.cbrt(x);document.getElementById('finalResult').innerHTML="∛"+x+" = "+result.toFixed(prec);}else{n=parseFloat(document.getElementById('input_n').value);if(isNaN(n)||n===0){alert('Please enter a valid non-zero degree n');return;}if(x<0 && n%2===0){document.getElementById('finalResult').innerHTML="Undefined (Even root of negative number)";return;}result=Math.pow(x,1/n);document.getElementById('finalResult').innerHTML=""+n+"√"+x+" = "+result.toFixed(prec);}if(showSteps){stepsText="
";stepsText+="Formula: r = x(1/n)
";stepsText+="x = "+x+"
n = "+n+"
";stepsText+="Calculation: "+x+"(1/"+n+") = "+result.toFixed(prec);document.getElementById('stepsOutput').innerHTML=stepsText;}else{document.getElementById('stepsOutput').innerHTML="";}}

Calculator Use

This square root calculator is a versatile tool designed to find the square root, cube root, or any nth root of a given number. Whether you are working on a simple geometry problem or complex algebraic equations, this tool provides instant and accurate results with customizable decimal precision.

By using this calculator, you can bypass manual long-division methods and focus on your higher-level mathematical concepts.

Choose a Root Type
Select between Square Root (default), Cube Root, or Custom nth Root to define the degree of the calculation.
Number (x)
The radicand, or the value you want to find the root of. This can be a positive integer or a decimal.
Root Degree (n)
Only visible for 'nth Root'. This represents the power to which the result must be raised to equal (x).

How It Works

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 × 5 = 25. The general mathematical relationship is expressed as:

√x = r such that r² = x

For higher-order roots like the cube root or nth root, the logic remains the same but with higher exponents:

  • Square Root: r = x1/2
  • Cube Root: r = x1/3
  • nth Root: r = x1/n

Calculation Example

Example: Find the square root of 144 using the square root calculator.

Step-by-step solution:

  1. Select "Square Root (√x)" from the dropdown menu.
  2. Enter "144" in the "Number (x)" field.
  3. Set decimal places to "0" for a clean integer result.
  4. Click "Calculate".
  5. The calculator identifies that 12 × 12 = 144.
  6. Result = 12

Common Questions

Can a negative number have a square root?

In the realm of real numbers, you cannot take the square root of a negative number because no real number multiplied by itself results in a negative value. However, in mathematics, we use "imaginary numbers" where the square root of -1 is represented by 'i'. Our square root calculator will denote these with an 'i' suffix.

What is a perfect square?

A perfect square is an integer that is the square of another integer. Examples include 1, 4, 9, 16, 25, 36, and 49. When you calculate the square root of a perfect square, you will always get a whole number result.

How do you calculate square roots by hand?

Manual calculation often involves the "Long Division Method" or the "Newton's Method" (also known as the Babylonian Method), which uses iterative guesses to get closer to the true value. Using an automated square root calculator is significantly faster and eliminates rounding errors during iterations.

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