Welcome! Today we'll learn how to write mathematical expressions in the form a plus b square root of 3. This is a standard form where a and b are rational numbers, and it's commonly used in algebra and number theory. Let's explore some examples of this form.
Now let's learn how to simplify expressions involving square root of 3. The key steps are: first, combine like terms; second, group rational and irrational parts separately; third, factor out square root of 3 where possible; and finally, write in the standard form a plus b square root of 3. Let's work through an example step by step.
Sometimes we encounter square root of 3 in the denominator of a fraction. To write this in our standard form, we need to rationalize the denominator. We do this by multiplying both the numerator and denominator by square root of 3. This eliminates the radical from the denominator and gives us the expression in the form a plus b square root of 3.
When multiplying expressions that contain square root of 3, we use the distributive property. Remember that square root of 3 times square root of 3 equals 3. After expanding, we collect like terms and write the result in our standard form a plus b square root of 3. Let's work through this multiplication example step by step.
Let's summarize the key points for writing expressions in the form a plus b square root of 3. First, simplify and combine like terms. Second, rationalize denominators when square root of 3 appears in the denominator. Third, use the distributive property for multiplication. Fourth, group rational and irrational parts separately. Finally, write in the standard form where both a and b are rational numbers. With practice, you'll master this important algebraic skill.