Square Root Property

Рет қаралды 28,179

4 жыл бұрын

www.greenemath.com/
mathematicsbyjgreene
In this lesson, we review the square root property. This allows us to solve quadratic equations of the form:
x^2 = k , (ax + b)^2 = k

Пікірлер: 31

@rnqtn 4 жыл бұрын

Was at a complete stop of progress but this video really cleared everything up. Thank you!

@Greenemath 4 жыл бұрын

Good luck with your studies :)

@felixtijerina7416 Жыл бұрын

100th attempt at college algebra, I feel like it's the only class standing in the way of my degree. You speak so clearly and I can't thank you enough for uploading videos. I could cry because I can now see a tiny light at the end of this forever tunnel. Thank you.

@Greenemath Жыл бұрын

Glad I could help! Just take it one topic at a time and you will achieve your goal. Good luck!

@bau5256 4 жыл бұрын

We're doing online class and the teacher can't teach properly because of weak Internet the math is so much harder right now. This is our subject a while ago and I didn't understand anything so thank you much 💗 I can do my homework now. God Bless you.

@Greenemath 4 жыл бұрын

I'm so glad it helped. Hopefully everyone can be back in the classroom soon. Good luck with your studies :)

@bau5256 4 жыл бұрын

@@Greenemath Thank you

@mccullymagloire9220 3 жыл бұрын

yes God bless you , you are a very clear and understanding teacher, the multiple problems is very helpful and the breakdown in many ways is better to remember

@Greenemath 3 жыл бұрын

Glad it was helpful!

@yuyuyu7252 3 жыл бұрын

What a Amazing Tutorial, better than my math teacher LoL my math teacher she teach a little bit faster, but you, you explain one by one, thank thank you so much for this vid, SORRY IF MY ENGLISH ARE NOT GOOD HEHEHE

@Greenemath 3 жыл бұрын

You're very welcome!

@HastiinTliziYazhi 5 ай бұрын

I wanted to double check my understanding that when we take the root of any single term we end up with both a positive and negative result. However, when we take the root of an expression such as (x-7)^2 we only end up with the expression, without the need for two solutions. My apologies if that is a silly concept, would you mind clarifying if that is incorrect?

@Greenemath 5 ай бұрын

There is some nuisance to this that is often not explained. sqrt[(x - 7)^2] = |x - 7| What ends up happening is that the above is baked into a rule known as the square root property. if x^2 = k , then x = ± k Where does that come from? sqrt(x^2) = sqrt(k) |x| = sqrt(k) x = sqrt(k) or x = -sqrt(k) This can be extended to your situation: (x - 7)^2 = 64 By the square root property: x - 7 = ±sqrt(64) Where does that come from? sqrt[(x - 7)^2] = sqrt(64) |x - 7| = sqrt(64) x - 7 = sqrt(64) or x - 7 = -sqrt(64)

@HastiinTliziYazhi 5 ай бұрын

Essentially, flipping signs on both the constant on the right side of the equation and the expression on the left side of the equation would be redundant at best. It is clearer, more simple, and easier to avoid silly mistakes if you only flip signs on the constant than flipping signs on the expression.

@Greenemath 5 ай бұрын

@HastiinTliziYazhi It would appear that you are lost, so maybe I can help. Let's start with something kind of basic and work our way up to the square root property. When we square a number, we lose information about the sign. (-2)^2 = 4 2^2 = 4 So when I have an equation such as: x^2 = 4 x = 2 or x = -2 This is the basis for the square root property. x^2 = k x = ± sqrt(k) A simple example. x^2 = 9 Using the square root property: x = ± sqrt(9) = ± 3 This is because x could be -3 or x could be +3, since squaring a number results in a loss of information about the sign. Okay, now for the other cases: (x - a)^2 = k Here it's the same thing, you are squaring a quantity now (x - a), so you are again losing information about the sign. x - a = ± sqrt(k) x = ± sqrt(k) + a Let's go back to the example: (x - 7)^2 = 64 x - 7 = sqrt(64) or x - 7 = -sqrt(64) x - 7 = 8 or x - 7 = -8 x = 15 or x = -1 Let's plug in now, I think this might make it makes sense: (15 - 7)^2 = 64 8^2 = 64 (-1 - 7)^2 = 64 (-8)^2 = 64 See how we ended up saying that 64 could come from -8 or +8?

@frexje6818 3 жыл бұрын

Yow this guy deserves 100k subs.:)))

@Greenemath 3 жыл бұрын

I'll be there in 2030 at this rate :)

@haileagstn4838 3 жыл бұрын

How did you subtract ten on the problem?

@Greenemath 3 жыл бұрын

What problem are you working on? Drop it in the comments and I will help you out! :)

@MSFR-911_ 2 жыл бұрын

Thank you so much

@Greenemath 2 жыл бұрын

You're most welcome

@patriciafagan56 3 жыл бұрын

I know this is late, but I am confused on the last problem. What happened to the minus 56 All the other problems I understand from your explanation?

@Greenemath 3 жыл бұрын

16x^2 - 56x + 49 is a perfect square trinomial, which means it can be factored into a binomial squared: 16x^2 - 56x + 49 = (4x - 7)^2 If you were to FOIL out (4x - 7)(4x - 7), you would get back to the 16x^2 - 56x + 49 at the beginning of the problem.

@patriciafagan56 3 жыл бұрын

@@Greenemath thank you, I get it now, the minus 56 is got from adding the two negative 7. Goodness do I feel stupid, but I’m glad I asked, it was driving me crazy😊

@Greenemath 3 жыл бұрын

@@patriciafagan56 You are very welcome. Let me know if you have other questions. 😎