Decimal Approximation Decimal Approximation EXPLORATION: Use your calculator to find a decimal approximation for each expression in the tables. Round to the nearest thousandth. What do you notice in the tables? Expression Decimal Approximation Decimal Approximation 2√3 + 3√3 5√3 8√2 – 5√2 3√2 4√7 + 9√7 13√7 Expression Decimal Approximation Decimal Approximation √7 + √3 √10 √25 + √9 √34 √17 - √5 √12

Operations with Radicals Algebra I ~ Unit 11

Addition and Subtraction of Radicals When adding or subtracting radicals, you must use the same concept as that of adding or subtracting “like terms.” In other words, the radicals must be the same before you add or subtract them.

Addition and Subtraction of Radicals If the radicals in your problem are different, be sure to check to see if the radicals can be simplified. EXAMPLE:

Simplify these:

Multiplying Radicals When multiplying radicals, you must multiply the OUTSIDE numbers and the INSIDE numbers separately, and then simplify (if possible). EXAMPLE:

Multiply and simplify these:

Expand and simplify these:

Dividing Radicals When dividing radicals, you must divide the OUTSIDE numbers and the INSIDE numbers separately, and then simplify (if possible). EXAMPLE:

Divide and simplify these:

Dividing Radicals Should a radical appear in the denominator of a fraction, it will need to be “removed” if you are trying to simplify the expression. To “remove” a radical from the denominator, we use a process called rationalizing the denominator: multiply the top and bottom of the fraction by the radical in the denominator. This creates a perfect square radical in the denominator. EXAMPLE:

Rationalize the denominator to simplify: