Square Root (โx) Practice Problems & Simplifying Radicals Step Solutions
The square root of a number x (denoted as โx) is the non-negative value y such that yยฒ = x. Master benchmark perfect squares 1โ20, radical simplifications (extracting largest square factors), and non-perfect square radical forms.
๐ง Core Problem-Solving Strategies
๐งฉ Perfect Square Benchmarks
Memorize key squares: 11ยฒ=121, 12ยฒ=144, 13ยฒ=169, 14ยฒ=196, 15ยฒ=225, 20ยฒ=400.
โก Product Property of Radicals: โ(aยทb) = โa ยท โb
To simplify โ48, factor into the largest perfect square: โ(16 ร 3) = โ16 ร โ3 = 4โ3.
๐ซ The "Divide by 2" Common Trap
Never divide by 2! โ36 is 6 (because 6ร6=36), NOT 18 (which is 36 รท 2).
โ Frequently Asked Questions
What is the principal square root?
The radical symbol โ always denotes the non-negative (principal) square root: โ25 = +5.
How do you simplify non-perfect square radicals like โ75?
Find the largest square factor of 75 (which is 25): โ75 = โ(25 ร 3) = โ25 ร โ3 = 5โ3.
Continue Learning & Practicing
Reinforce your understanding with printable worksheets, step-by-step guides, calculators, and speed games: