A surd is a square root that cannot be reduced to a rational number, such as √5. While calculators provide approximations of surds, it is better to leave them in radical form for exactness. Indices are a way to express large numbers using exponents, with laws for manipulating expressions that share the same base. The six laws of indices are: 1) any number to the 0 power is 1, 2) negative exponents become reciprocals, 3) multiplying expressions adds the exponents, 4) dividing expressions subtracts the exponents, 5) raising an expression to a power multiplies the exponents, and 6) roots can be expressed with fractional exponents.