I was really good at math in school, but I pursued music as my college major. (math + music = music theory, my best music subject). They say "Follow your dream, and the money will follow." Not always. LOL Anyway, I had not factored a polynomial or dealt with trigonometry in decades, but I find myself needing to help my stepdaughter with her math homework. I watch your videos, and I go, "Oh, I remember that... yes, and I remember that now..." and I can help her with everything - so thanks. Still, I never forgot the quadratic equation - 40 plus years later, my stepdaughter is amazed that I can just rattle it off! LOL
Well, I haven't done this since leaving school in 1969 and I do not remember doing it at all, however it was obvious to me that only d was large enough. Working it out without a calculator however in my head without pencil or paper, which is what I like to do, I got stuck. So I enjoyed your solution, and before you finished I had it figured out. Thanks John.
Super simple if you remember that fraction exponents mean the numerator is a power and the denominator is the root. This is just the number two raised to the 7 1/2 power. 7 does not evenly divided by two so we are left with three and the remainder of 1/2. 2 cubed is 8 multiply that by the square root of 2 which gives you d.
That alternate solution at the end was a way of looking at the problem which, when first looking at the problem, I quickly dismissed. Now I see that angle of attack would have borne fruit. Also I was initially intimidated by the parentheses but I see I needn't have been. So I learned a couple things! 😀
Greetings. The answer is 8(2^1/2). (2^12)^7=(2^7)^1/2=(128)^1/2= (64^1/2×2^1/2)=8×(2^1/2)= 8 times the square root of 2. Alternatively, we could say (2^1/2)^7= (2^1/2×2^1/2)×(2^1/2×2^1/2)×(2^1/2×2^1/2)×(2^1/2)= (2^1/2+1/2)×(2^1/2+1/2)×(2^1/2+1/2)(2^1/2)= (2^1×2^1×2^1×2^1/2)= 2^3×2^1/2=8×2^1/2.
√2 × √2 = 2 (√2)⁷ is √2 × √2 × √2 × √2 × √2 × √2 × √2 That's three pairs of √2 with one √2 left over. Each pair √2 × √2 equals 2, so we're multiplying three lots of 2 = 8 then finally multiplying the one √2 that is left over. So the answer is 8√2. You don't need to explain that √2 × √2 = 2. That is literally the definition of a square root. If you're pitching this at people who might not immediately know that √2 × √2 equals 2, then going into a more step by step explanation of how to calculate √2 × √2 is completely misconceived. What you need is a section in the video where you explain what "square root" means. If you're expecting people to come into this video not knowing what "squate root" means, and by the end you haven't explained what "square root" means, then that is a massive hole in your teaching.
4 minutes 30 in the video! WHAT ARE YOU DOING???!!! √2 × √2 is obviously 2. That's the DEFINITION of a square root! You don't need to go via √2 × √2 = √(2×2). Do you not care at all about your students actually understanding this stuff?
I try to work the problem through before playing any of the video. Then skip to the very end to check my answer. I rarely watch the lesson, only if I need a refresher. Do skip forward over the intro, watching it once is good forever, and any other part you don't care to watch. You do the same with commercials don't you?
I was really good at math in school, but I pursued music as my college major. (math + music = music theory, my best music subject).
They say "Follow your dream, and the money will follow." Not always. LOL
Anyway, I had not factored a polynomial or dealt with trigonometry in decades, but I find myself needing to help my stepdaughter with her math homework.
I watch your videos, and I go, "Oh, I remember that... yes, and I remember that now..." and I can help her with everything - so thanks.
Still, I never forgot the quadratic equation - 40 plus years later, my stepdaughter is amazed that I can just rattle it off! LOL
Well, I haven't done this since leaving school in 1969 and I do not remember doing it at all, however it was obvious to me that only d was large enough. Working it out without a calculator however in my head without pencil or paper, which is what I like to do, I got stuck. So I enjoyed your solution, and before you finished I had it figured out. Thanks John.
Thx for refresher.
got it D fun just multiply them sr2 x sr2 =2 2 x 2 x 2 x sr2 = 8sr2 thanks for the fun
You always find a longer path .
Super simple if you remember that fraction exponents mean the numerator is a power and the denominator is the root. This is just the number two raised to the 7 1/2 power. 7 does not evenly divided by two so we are left with three and the remainder of 1/2. 2 cubed is 8 multiply that by the square root of 2 which gives you d.
Same process and same answer.
Thank you
Nice! Thanks!
What's required here is to
Convert:
sqrt(2) = 2^(1/2)
Then:
[sqrt(2)]^7 = [2^(1/2)]^7
= (2)^(7/2)
Since
(x^a)(x^b) = x^(a+b)
so
= (2)^(6/2)×(2)^(1/2)
= (2)^3 × (2)^(1/2)
= 8 sqrt(2)
PROOF:
sqrt(2)×sqrt(2)×sqrt(2)×sqrt(2)
×sqrt(2)×sqrt(2)×sqrt(2)
= [sqrt(2)]^2×[sqrt(2)]^2
×[sqrt(2)]^2×[sqrt(2)]
= 2 × 2 × 2 × sqrt(2)
= 8 × sqrt(2)
That alternate solution at the end was a way of looking at the problem which, when first looking at the problem, I quickly dismissed. Now I see that angle of attack would have borne fruit.
Also I was initially intimidated by the parentheses but I see I needn't have been.
So I learned a couple things! 😀
Don't be afraid of parentheses. They are tools that can make your life way easier. Learn to like, even love parentheses.🥰
Good stuff Mr J
🙏👋👍❤️💪🌎
d) 8*2^1/2
(2^1/2)^6 x 2^1/2
2x2x2x2^1/2
8x 2^1/2
(✓2)^7 = 2^(0.5 * 7) = 2^3.5 = 8✓2
Alternate way :
(✓2)^7 = ✓2*✓2*✓2*✓2*✓2*✓2*✓2 Combine each pair of roots → (✓2*✓2)*(✓2*✓2)*(✓2*✓2)*✓2 = 2*2*2*✓2 = 8✓2
Thank you so much. I am not here for the quick answer I am here to learn the process.
1.41
A lot of ways to do this. Simplify to 2^(7/2) which is 2^(3.5) which is 8 times sqrt 2.
The answer is (d)
👍👍
d. in about nine seconds in my head. Fun one.
d) 8 sq.root2
d)Answer
(Sqrt(2)) ² = 2
(Sqrt(2)) ⁶ = 2³ = 8
Now multiply both sides by sqrt(2)
(Sqrt(2))⁷ = 8 Sqrt(2)
Answer is D
2^5
Greetings. The answer is 8(2^1/2).
(2^12)^7=(2^7)^1/2=(128)^1/2=
(64^1/2×2^1/2)=8×(2^1/2)=
8 times the square root of 2.
Alternatively, we could say (2^1/2)^7=
(2^1/2×2^1/2)×(2^1/2×2^1/2)×(2^1/2×2^1/2)×(2^1/2)=
(2^1/2+1/2)×(2^1/2+1/2)×(2^1/2+1/2)(2^1/2)=
(2^1×2^1×2^1×2^1/2)=
2^3×2^1/2=8×2^1/2.
2^7/2
Ans=8√2. (√2)^7=(√2)^6•√2. ={(√2)^2}^3•√2=2^3√2=8√2.
8√2
D)
D
8rt2
8 i/2
a) 8
It takes 10 secs to solve this not 14 mins
this video is not for you then
For some people it will take a lifetime to figure this problem out.
You should move on to the calculus channel.
It took you ten whole seconds? Why so slow ?
Show off!
Show off!
√2 × √2 = 2
(√2)⁷ is
√2 × √2 × √2 × √2 × √2 × √2 × √2
That's three pairs of √2 with one √2 left over. Each pair √2 × √2 equals 2, so we're multiplying three lots of 2 = 8 then finally multiplying the one √2 that is left over. So the answer is 8√2.
You don't need to explain that √2 × √2 = 2. That is literally the definition of a square root. If you're pitching this at people who might not immediately know that √2 × √2 equals 2, then going into a more step by step explanation of how to calculate √2 × √2 is completely misconceived. What you need is a section in the video where you explain what "square root" means.
If you're expecting people to come into this video not knowing what "squate root" means, and by the end you haven't explained what "square root" means, then that is a massive hole in your teaching.
11.3137
√2 = 2^½ so (√2)^7 = 2^(½ × 7) = 2^3.5 = 11.31
8√2 = 11.31
thus, D
(2^½)^7= (2^⁷)^½ = 128^½ =(64×2)^½ = 8(2)^½ the answer is d) 8(2)^½
dis right
4 minutes 30 in the video! WHAT ARE YOU DOING???!!!
√2 × √2 is obviously 2. That's the DEFINITION of a square root! You don't need to go via √2 × √2 = √(2×2).
Do you not care at all about your students actually understanding this stuff?
Why is he so slow ? He learns the maths and often not as he should :)
8root 2
D.
Sqrt(2)^6 = 2^3 conclude result = 8* sqrt(2) thats all
This can be solved in less than a minute, but you have taken 14 minutes!
(2sqrt )^7= make 7 an even number 6= (2sqrt)^6.2sqrt.= 8sqrt2 ans.
d)
Without watching this, I feel there is going to be a lot of face-palming by people when you reveal the answer. 🤣
√2⁶ = 2³ = 8, so √2⁷ = 8√2.
This takes two seconds, and he talks about it for 14 minutes.
I solved this one while finishing my bowl of corn flakes.
8
14
Many will get wrong!
Not so! Just say it silently! Is there anything better to hear?
“YOU TALK TOO MUCH”
Maybe you have A.D.D. ?
I try to work the problem through before playing any of the video. Then skip to the very end to check my answer. I rarely watch the lesson, only if I need a refresher. Do skip forward over the intro, watching it once is good forever, and any other part you don't care to watch. You do the same with commercials don't you?
D
D
D