Radical Calculator
Type a square root or radical expression and this calculator simplifies it to its exact form, plus a decimal value.
Use sqrt(n) for a square root, e.g. sqrt(48) simplifies to 4*sqrt(3). You can also use + and * with other roots, e.g. sqrt(8)+sqrt(2).
How to simplify a radical by hand
- Find the largest perfect square (4, 9, 16, 25, 36…) that divides the number under the root.
- Split the root into that perfect square times what's left: √48 = √16 × √3.
- Take the square root of the perfect square out the front: √16 = 4, giving 4√3.
Worked example
Simplify √72: the largest perfect square factor of 72 is 36 (72 = 36 × 2), so √72 = √36 × √2 = 6√2, which is about 8.485.
Practise the algebra behind this in the Simplify Calculator or see every formula worked through in Maths Formulas.
Frequently asked questions
How do you simplify a square root?
Find the largest perfect square that divides the number, then split it: √48 = √(16 × 3) = √16 × √3 = 4√3.
What is a radical in maths?
A radical is a root symbol, usually a square root (√), but it can also be a cube root or higher. The number inside is the radicand.
Can you add square roots together?
Only if they have the same number under the root (like terms): 2√3 + 5√3 = 7√3. √8 + √2 first simplifies to 2√2 + √2 = 3√2.
What is the decimal value of √48?
√48 = 4√3 ≈ 6.928.
