Free Maths Calculator

Surds Calculator

Simplify surds, multiply them, and rationalise denominators, keeping every answer exact instead of reaching for a decimal. Square factors are hunted down and named, and the rationalising step shows why multiplying by root a over root a is allowed: it is just multiplying by one.

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Answer

Method, Step by Step

    Worked Example

    Simplify √48.

    1. Find the biggest square factor:48 = 16 × 3
    2. Split the root:√48 = √16 × √3 = 4√3

    Answer: 4√3

    Try These Yourself

    Simplify √50.Show answerHide answer

    Answer: 5√2

    50 = 25 × 2.

    Work out √8 × √2.Show answerHide answer

    Answer: 4

    √16 = 4.

    Rationalise 6/√3.Show answerHide answer

    Answer: 2√3

    6√3 ÷ 3 = 2√3.