Online Radical Simplification Calculator (Square Root √)

This calculator lets you simplify a square root by extracting the perfect square factors. It is ideal for students and anyone who wants to understand the radical simplification process.

How to use the calculator?

• Enter a positive whole number in the input field. This number is the radicand of the square root you want to simplify.
• The simplified result is displayed automatically in the result field. If the number is a perfect square, the exact square root is shown. Otherwise, the simplified form of the radical is displayed.
• Click the Steps button to see the detailed simplification steps, including the perfect square factors that were extracted and the intermediate steps of the calculation.
• Use the Clear button to reset the fields and perform a new simplification.

Steps to simplify a square root

With the Steps button, you can follow the simplification process step by step. Here are the general steps the calculator follows:

• Identify the factors of the entered number.
• Determine which factors are perfect squares (1, 4, 9, 16, 25, etc.).
• Extract the square roots of the perfect square factors.
• Multiply the extracted roots by the remaining factors under the radical to obtain the simplified form.

Square root simplification examples

• √18 ➜ 3√2 (because 18 = 9 × 2 and √9 = 3)
• √50 ➜ 5√2 (because 50 = 25 × 2 and √25 = 5)
• √72 ➜ 6√2 (because 72 = 36 × 2 and √36 = 6)
• √100 ➜ 10 (because 100 is a perfect square and √100 = 10)

Why simplify a square root?

Simplifying square roots is a fundamental skill in mathematics, particularly in algebra and geometry.

It makes expressions easier to manipulate and understand, especially when working with equations or functions involving radicals.

Save

The Save button lets you keep the calculations you make. You can save a number and its simplified root, then export them in PDF or CSV format.

Shortcuts

m ⇝ Clear

f ⇝ Save