Roots and Exponents

Question 1

Shortcut for Nested Radicals.

What is the SHORTCUT rule for solving NESTED RADICALS.
√5 √5 where r = INDEX of the RADICAL and n = number of such RADICALS.

Answer 1

x ^ 1/r^n

Question 2

Comparing Numbers with Large Exponents

How do you SIMPLIFY numbers raised to LARGE EXPONENTS?

Answer 2

1. Find the GCF of the EXPONENTS.
2. Use the GCF as the RADICAL and take the ROOT of each EXPONENT.
3. Calculate the SIMPLIFIED exponents.

Question 3

Mutliplying Mixed Radicals

How do we MULTIPLY 2√6 * 2√6.

Answer 3

2 √6 * 2 √6 = 4 * 6 = 24.

Question 4

Comparing Radicals

When comparing RADICALS with different INDICES, how do you SIMPLIFY the RADICAL?

Answer 4

Step 1: convert each radical to a power of a fraction.
Step 2: find the LCD of each of the fractions.
Step 3: raise the powers of fractions to the power of the LCD.
Step 4: Simplify the exponent.