How to Find Double Square Roots

By Tricia Lobo

In algebra, you will receive your first introduction to double square roots. Although such problems might look complicated, questions involving double square roots are just intended to test your understanding of the properties of square roots. Therefore, assuming you have such an understanding, these questions should be quite simple and fun.



Resolve the first square root, or the square root within the square root. If the problem is sqrt(sqrt(49)), resolving the first square root allows us to simplify the expression to sqrt(7). If the problem is sqrt(sqrt(42-6)), then resolving the first square root gives us sqrt(sqrt(36)), or sqrt(6).

Resolve the second square root. In each of our examples, you will need to use a calculator to find the value of sqrt(7) or sqrt(6): both are fractional.

Square the value that you compute in Step 2 twice. After you square the value twice, you should obtain the value within the first square root.

About the Author

Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.