Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Number
Powers and Roots
What is Powers and Roots?
A power is the result of multiplying a number by itself a stated number of times, written with an index; a root is the inverse operation, so the nth root of a number is the value which, raised to the power n, returns it. The principal square root of a non-negative number is itself non-negative, which is why the square root of x squared equals the modulus of x rather than x.
This definition is part of the Number chapter in Cambridge O Level Mathematics (Syllabus D).
Powers and Roots in context
Powers and roots are inverse operations, and on Paper 1 a large part of the work is recall rather than calculation. Knowing \(13^2=169\) instantly turns \(\sqrt{169}\) into a one-second answer, and recognising \(288=144\times2\) is what makes \(\sqrt{288}=12\sqrt2\) possible without a calculator. The recall table below is assumed knowledge; the rest of Topic 1 leans on it constantly.