Square Roots
Grades 8–10 Algebra Roots
The square root asks: "what number times itself gives this?" √25 = 5 because 5·5 = 25. It's the inverse of squaring — the exponent run backwards.
Perfect squares to memorize
√1=1 √4=2 √9=3 √16=4 √25=5
√36=6 √49=7 √64=8 √81=9 √100=10 √144=12
Estimating roots that aren't perfect
√30 sits between √25 = 5 and √36 = 6, closer to 5 (30 is nearer 25 than 36). Actual: ≈ 5.48.
Simplifying roots
If a perfect square hides inside, pull it out:
√50 = √(25·2) = √25 · √2 = 5√2
√72 = √(36·2) = 6√2
√12 = √(4·3) = 2√3
Watch out
√(a + b) is not √a + √b. √(9 + 16) = √25 = 5, but
√9 + √16 = 3 + 4 = 7. Roots split over × and ÷ only.
Practice
√81 = ___
√50 is closest to:
Simplify √12 (write like 2√3)
√(9 + 16) = ___
Next: polynomials · Back: exponents