Surds and Indices

Master exponent operations (indices) and rational roots (surds). Visualize square factors geometrically and trace how fractional exponents map to exponential curves.

Interactive Sandbox

Surd & Power Explorer

Toggle between simplifying radical surds geometrically on the grid, or plotting indices and power curves on the coordinate plane.

Surd Square Factoring Grid

Active Surd

√12 = 2√3

Radicand Value (N) 12

Shaded grids inside the canvas denote the largest perfect square factor that can be rooted outside the radical.

Algebraic Solver

Laws of Exponents & Radicals

Study the mathematical properties that govern exponential indices and radical simplifying.

Factorizing the Radical

Exponents & Radicals Laws

Product Law x^a • x^b = x^{a + b}
Quotient Law x^a / x^b = x^{a - b}
Power of a Power (x^a)^b = x^ab
Fractional Exponent x^a/b = ^b√x^a

Evaluation

Conceptual Quiz

Test your understanding of exponents, laws of indices, and surd simplification.

Question 1 of 5 Score: 0/0

Simplify the surd √72 into its simplest radical form.

Correct Answer!

Explanation text goes here...

Indices & Surds Cheatsheet

Simplifying: Pull out perfect squares: √(A² • B) = A√B
Negative Index: x^-p = 1 / x^p
Fractional: x^1/2 = √x, x^1/3 = ³√x
Zero Exponent: x⁰ = 1 (for x ≠ 0)