Mistake of the week-3

Math Vocabulary:

Mixed radical– Radicals expressed in the form ““, all mixed radicals can be converted into entire radicals. Mixed radicals are most of the time used to express large radicals in their simplest form. Ex: , if it was an entire radical it would be

Entire radical– Radicals expressed in the form ““. You can transform entire radicals to mixed radicals if there are perfect sections while factoring the radicand.

Radical– An expression containing the radical sign (square root symbol).

Radical sign– √.  The square root sign is called “radical sign.”

Coefficient– Number that represents a constant value, usually multiplies the expression.

Index– A number located at the top left of the radical sign, it determines what type of root the expression is using. If there is no index we assume it has an index of 2 (square root).

Radicand– Number inside the radical sign.

Factorize/ factor/ factoring– In math factoring or to factor is to find the smallest numbers that multiplied together will give you the original number. This is used so you can work with simpler and smaller numbers.

Ex: 250= 25 x 10, you can still make those numbers smaller, 25= 5 x 5 and 10 = 2 x 5.

Therefore it will end up being 250 = 5 x 5 x 2 x 5.

Like terms– Terms that have the same base and same exponent. Ex: x and x^2 are not like terms because they do not share the same exponent. xy^3 and 4xy^3 are like terms because their variables and exponents are the same (the coefficient is the only thing that can different in like terms)

Best mistake of the week:

Workbook Page 62, number 7:

My mistake:

Adding and subtracting radicals was the new thing we learned this week, I did this math problem after that first lesson and it was challenging. My mistake is that I over complicated the problem.

Why is this important? 

In math you are looking to be as efficient as possible. The best thing to do when there is a difficult problem is to analyze the wording/ image/ equation/ etc. However, we usually overthink those math problems that look complicated, this can backfire during a test, making you lose time and get nervous.

What I did:

Instead of taking the time to analyze the picture I made up lines and tried solving it with my own logic.

Instead of looking at the figure as a rectangle I assumed that it was a square and that missing parts were the originals but divided by half. This clearly did not work because even though it looks like we are diving the full length by half, we do not know the measurements plus we still have not learned how to divide radicals.

Solution:

Adding and subtracting radicals:

Step 1. You can only add or subtract radicals that are like terms. To do this you have to simplify these radicals and/or convert them into mixed radicals.

Step 2. After you have simplified all your radicals, you can use them to add or subtract with your other radicals. When doing this remember that the only thing that changes are the coefficients (the roots will stay the same).

Remember- Only add and subtract like terms, do not worry if it is a two radical answer because they usually are.

The easy way to solve this problem was to take both values and subtract them-

x= +

y= –

This is the right answer.

Remember to always take the time to analyze the question.