Math HL

Radicals: Anything with the radical sign Surds: Irrational Radicals

By defnition, sqrt(x) is the non negative number such that sqrt(x) ^ 2 = x

Rationalizing the denominator, multiplying by a square root that makes up 1, or multiplying by conjugates.

Law of exponents:

1. Quotient of Powers: a^m / a^n = a^(m - n)
2. Product of Powers: a^m * a^n = a^(m + n)
3. Power of a Power: (a^m)^n = a^(m * n)
4. Power of a Product: (a * b)^n = a^n * b
5. Power of a Quotient: (a / b)^n = a^n / b
6. Zero Exponent: a^0 = 1 (where a ≠ 0)
7. Negative Exponent: a^(-n) = 1 / a^n (where a ≠ 0)