Radical simplification
Product and Quotient rule
Let be a positive integer number, and let and be two real numbers, such that and are well defined. Then:
- .
- ; provided that .
Simplified form
Square root:
A square root radical is in simplified form if it complies the following three conditions:
1. The number under the radical (radicand) has no factor, but 1, that is perfect square.
2. Radicand has no fractions.
3. No denominator has radicals.
root:
An root radical is in simplified form if the following three conditions are met:
1. The number under the radical (radicand) has no factor, but 1, that is an power.
2. Radicand has no fractions.
3. No denominator has radicals
Guidelines to simplify a radical
Square root:
- Factor out the coefficient as the product of the highest perfect square that divides it and a number that is not a perfect square.
- Write the variables as a product of the highest even power less than the exponent, and an odd power.
- Take square root of the perfect squares.
- Factor out the coefficient as the product of the highest power that divides it and a number that is not an power.
- Write the variables as a product of the highest power less than the exponent, and the difference between the exponent and the power.
- Take root of the powers.
Formative assessment
Use the following applets to practice simplifying radicals.
References
Brzezinski, T. (2016, September 2). Simplifying radicals (i). GeoGebra. https://www.geogebra.org/m/g7UAQHDK.
Brzezinski, T. (2016, September 2). Simplifying radicals (ii). GeoGebra. https://www.geogebra.org/m/nufHUrek.
Miller, C. D., Heeren, V. E., Hornsby, J., & Heeren, C. (2020). Mathematical ideas. Pearson Education, Inc.