TASC Math Exam—Solving Radicals - dummies

The TASC Math exam will likely contain some questions where you’ll have to confront radicals. Don’t worry—it’s not as scary as it sounds. You can just think of radicals as the “opposite” operation of applying exponents.

The symbol

is called a radical or root. Unless otherwise indicated, you’re looking for the

or principal root when it’s an even index (the number outside the root symbol). Otherwise, you must consider both the positive and negative versions:

Note that if the index of the radical is not explicitly written, then you assume it’s the square root, so the index is 2.

It’s important to remember perfect squares. You should probably know up to 12 at least, if not 15.

1. Make a factor tree (go to the primes, meaning you can’t break the number down anymore).
2. Find pairs (square root), triples (cubed root), and so on.
3. Write pairs outside the radical (write only once) and leave everything else inside (think of the pairs as friends going out to play).
4. Find the products of what you “pulled out” and left behind.

Take this example:

## Practice questions

1. Solve for x:
2. Simplify