To find the simplest radical form, factor the number (radicand) under the radical to find perfect square factors (or perfect cubes for a cube root, etc.), pull the roots of these perfect factors out front, and leave any remaining non-perfect factors inside the radical, ensuring the radicand has no more perfect factors and no radicals are in the denominator.
How to simplify a radical expression using the Product Property
In order to simplify a radical:
What is the square root of 48 in simplified form? The square root of 48 in simplified form is 4√3.
Square Root of 75 by Prime Factorization Method
The prime factorisation of 75 is 3×5×5. Thus, √75 = √3. √5. √5 = 5√3.
The number 75 is not a perfect square because it cannot be expressed as the product of an integer multiplied by itself. Its prime factors (3 and 5²) do not form perfect pairs for all primes, leaving an irrational square root.
Solve Radical Equations
Simplified radical form of the square root of 45
Hence, square root of 45 can be expressed as, √45 = √(9 × 5) = 3√5. 45 is not a perfect square, hence, it remains within roots. The simplified radical form of the square root of 45 is 3√5.