OBJECTIVES: STUDENTS WILL BE ABLE TO… EVALUATE NTH ROOTS OF REAL NUMBERS USING RADICAL NOTATION AND RATIONAL EXPONENT NOTATION. 7.1: N TH ROOTS AND RATIONAL EXPONENTS

n th ROOT OF a If b n = a, then b is the n th root of a 3 3 = 27, 3 is the cube root of = 16, 2 is the 4 th root of 16 RULE: n is called the “index”. It tells you what root you are taking. EX:

REAL N TH ROOTS Let n be an integer > 1, and let a be a real number: If n is odd, then a has 1 n th real root: If n is even, and a > 0, then a has 2 real n th roots: If n is even and a = 0, then a has 1 n th root If n is even and a < 0, then a has no real n th roots no real roots

FIND THE INDICATED N TH ROOT(S)

RATIONAL EXPONENTS Can rewrite a radical expression with rational exponents. They are one in the same! Example: OR

USING NEGATIVE EXPONENTS

EXAMPLES Rewrite using radical notation: Rewrite using rational exponents:

EVALUATE:

USING YOUR CALCULATOR TO EVALUATE Enter 3 ^ (3 / 4)

SOLVING EQUATIONS USING N TH ROOTS Isolate the quantity raised to the n th power, and take the n th root of both sides. Be careful…. If n is odd, 1 solution In n is even, 2 solutions (±)

EXAMPLES: SOLVE

EXAMPLE A basketball has a volume of about in 3. The formula for the volume of a basketball is V = r 3. Find the radius of the basketball.

EXAMPLE The rate r at which an initial deposit P will grow to a balance A in t years with interest compounded n times a year is given by Find r if P = $1000, A = $2000, t= 11 years, and n = 12