On this page, we hope to clear up problems that you
might have with square roots and their uses. Square
roots are something you'll never get away from. Reassuring,
aren't we? :-) Scroll down or use the links below to start
understanding square roots better!
Addition and Subtraction of square roots
Multiplication of square roots
Quiz on Square Roots
square roots, keep the Product of Square Roots Theorem in mind.
It is outlined below:
1. Simplify: SQRT(50)
Adding and subtracting square roots is just like combining like terms when you need to do that with algebraic expressions. If the indeces (a square root's index is 2, a cube root's index is 3, a 4th root's index is 4, etc.) or the radicands (the expression under the root sign or enclosed by parentheses after SQRT) are the same, you have a like term on your hands.
1. Add: (4 * SQRT(2)) - (5 * SQRT(2)) + (12 * SQRT(2))Many times, such problems will not be given to you with all the terms alike, or even trickier, the terms will only look different!
1. Simplify: SQRT(18) + SQRT(8) Solution: Write each square root as a product of prime factors.
Instead of using the Product of Square Roots Theorem to separate a root, we can use it in reverse to multiply radicals, as the following example shows: SQRT(2) * SQRT(3) = SQRT(6)
1. Simplify: 4(SQRT(3)) * 3(SQRT(2))
Take the Quiz on square roots. (Very useful to review or to see if you've really got this topic down.) Do it!