Math / Radicals
Simplify radicals, extract perfect-square factors, and rationalize a square-root denominator.
Radical worksheet
Inputs
Enter a nonnegative radicand. Optional fraction fields rationalize numerator divided by the square root of the denominator.
Integer radicands are factored exactly. Non-integer radicands remain under the radical in exact notation and also receive a decimal approximation.
Result
Exact form
6√2
Decimal approximation
8.4853
Rationalized fraction
Not requested
√72Start with the positive real square root of the entered radicand.
√72 = 6√2Rewrite the radicand as a perfect square times a square-free factor, then take the square root of the perfect square.
Simplifies square roots of nonnegative numbers by extracting perfect-square factors, shows a decimal approximation, and optionally rationalizes a denominator such as 3/√12.
Students simplifying radicals, teachers checking exact forms, and anyone who needs both an exact radical and a readable decimal approximation.
For an integer radicand, the calculator factors out the largest square factor: √(m²n) = m√n. For an optional denominator, it multiplies by the matching radical and reduces the resulting fraction.
Exact factor extraction is provided for integer radicands in the supported range. Non-integer radicands are shown as an exact unevaluated radical plus a decimal approximation; complex roots are not used.
Factor the radicand into a perfect square times a square-free remainder, take the square root of the perfect square, and leave the remainder under the radical.
It is an integer with no perfect-square factor greater than 1. For example, 2 is square-free in 72 = 36 × 2.
Multiply the numerator and denominator by the radical in the denominator. Then simplify any square factors and reduce the integer fraction.
No. The real square-root function is defined for nonnegative radicands. A negative input needs complex-number methods that this calculator does not provide.
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Math / Radicals
Simplify radicals, extract perfect-square factors, and rationalize a square-root denominator.
Radical worksheet
Inputs
Enter a nonnegative radicand. Optional fraction fields rationalize numerator divided by the square root of the denominator.
Integer radicands are factored exactly. Non-integer radicands remain under the radical in exact notation and also receive a decimal approximation.
Result
Exact form
6√2
Decimal approximation
8.4853
Rationalized fraction
Not requested
√72Start with the positive real square root of the entered radicand.
√72 = 6√2Rewrite the radicand as a perfect square times a square-free factor, then take the square root of the perfect square.
Simplifies square roots of nonnegative numbers by extracting perfect-square factors, shows a decimal approximation, and optionally rationalizes a denominator such as 3/√12.
Students simplifying radicals, teachers checking exact forms, and anyone who needs both an exact radical and a readable decimal approximation.
For an integer radicand, the calculator factors out the largest square factor: √(m²n) = m√n. For an optional denominator, it multiplies by the matching radical and reduces the resulting fraction.
Exact factor extraction is provided for integer radicands in the supported range. Non-integer radicands are shown as an exact unevaluated radical plus a decimal approximation; complex roots are not used.
Factor the radicand into a perfect square times a square-free remainder, take the square root of the perfect square, and leave the remainder under the radical.
It is an integer with no perfect-square factor greater than 1. For example, 2 is square-free in 72 = 36 × 2.
Multiply the numerator and denominator by the radical in the denominator. Then simplify any square factors and reduce the integer fraction.
No. The real square-root function is defined for nonnegative radicands. A negative input needs complex-number methods that this calculator does not provide.
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