Using radicals as needed

An instruction to use radicals as needed usually asks you to keep an exact answer involving roots when the value does not simplify to a rational number. It does not usually mean that every answer must contain a radical.

Meaning and context

Look for a perfect-square factor when simplifying a square root. For √72, write 72 as 36 × 2, giving 6√2. Since two has no larger perfect-square factor, this is the usual simplified radical form.

Examples and usage

If a calculation produces √49, the result is seven, with no radical needed. If it produces √22, leaving √22 preserves the exact value. A decimal such as 4.69 is an approximation rather than the same exact expression.

What to check

Follow any additional directions about rationalizing denominators, complex numbers, or rounding. An instruction’s precise scope depends on the exercise. Show the factorization or equation step so that the final radical is justified rather than merely copied from a calculator.

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