Radical Notation

Algebra 1 · Axiom Academy

Read the parts of a root symbol, see how the index counts equal factors, and meet the bridge to fractional exponents. Every radical has three pieces. The radical sign says take a root. The radicand is the number tucked under it. And the small index in the notch tells you which root — how many equal factors you are looking for. The square root of a is the value that, multiplied by itself, gives a . Index 2 means two equal factors. Geometrically, is the side length of a square whose area is 16 : the side grows until , and it lands on 4 . The cube root of a is the value used three times in multiplication to make a — index 3 . Think of as the edge length of a cube of volume 8 : three copies of the edge 2 multiply to fill the cube, and . The pattern keeps going. The n th root is the number that, raised to the n th power, equals a . The index n is simply a count: it tells you how many equal factors must multiply together to rebuild the radicand. Index 2 , 3 , 4 , 5 — any positive integer works. 5. The Bridge to Fractional Exponents Here is the key insight: a radical is a fractional exponent. Taking the n th root is the same as raising to the power — the index slides down to become the denominator of the exponent. The n th root of a is a raised to the power You can now read a radical, use the index to count equal factors, and rewrite any root as a fractional exponent. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Algebra 1 course.