Simplify the square root of (4/7 times 14/3) =? UNDERSTAND Square Roots?

How simplify the square root of a fraction - perfect squares and rationalize the denominator.

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[Xnocturnus]

You Sir, are like the Bob Ross of mathematics -- soothing away confusions in an amiable manner...wish I had you as a maths tutor in my schooling years! 😌

[thl.e]

Thank you! Appreciate your teaching. Blessings

[billydickens]

This year has been 50 years out of school. Thank you alot of refresh

[bravewave]

This is good exercise for the brain. 🎉

[juliehardy]

Thank you I am 66 this year and still am up for learning 👍

[andrewg.carvill]

Math problems that ask you to 'simplify' always remind me of a math teacher I had who ruled the class by sarcasm. I was sent to the board to solve a 'simplify' problem in front of the class, but instead of the thing getting smaller the way it was supposed to, it just got bigger and bigger. After 5 minutes of struggle, the teacher's voice resounded from the back of the class: "READ the question, Carvill. It says SIMPLIFY, not COMPLICATE!". By mutual agreement I was demoted to 'pass' math by the end of the week, so in a way I had managed to 'simplify' two people's problems: mine and the teacher's.

[quigonkenny]

(2√6)/3

What's under the radical simplifies quite easily to √(8/3) or √8/√3. This simplifies to (2√2)/√3. Can't have a radical in the denominator, though, so we multiply by √3/√3 and get (2√6)/3.

[kaydonahue]

My friend was making Ds in post graduate classes. I imagined shooting arrows into an A target. My friend asked me to help her learn how to choose multiple choice answers. We talked 3 hours over the phone every night. I taught her that you have to learn that three of the answers may be partially correct. One will be completely correct. Finally she caught on. She made a B. I made an A. Of 1500 students who started the two year program. 500 made it into the second year. 30 got jobs. We both were hired. She was from Pakistan. She was taught how to give oral, and written essays in British schools. I knew the books orally, backwards and forwards by explaining all the answers, jumping back and forth through the pages to answer every one of her questions. So few made it. We saved each other. I had four new teaching certificates, which raised my salary, and earned yearly stipends, but it was like going through boot camp, working, going to school, taking care of two kids, and studying three hours a night. I always taught my own kids what they did not understand, no matter what time of night.

[bigdog]

a little different then what I did. I recognized that 8 is the same as 4 * 2. So I factored the numerator to 2(sqroot(2)) divided by sqroot(of 3). Then I multiplied the unfactored 2 by 3 and reduced the denominator to 3. (sqroot of (n) x sqroot of (n) is just n). this of course left me with (2 x sqroot(6) / 3) which is the answer.

[NatureinActionJGM]

Love your method of teaching, I'm also here to just ask what is that awesome chalkboard you're using :-) ?

[ianchapman]

I am a math and a physics teacher, and I don't see why you can't have an irrational number in the denominator (other than older math teachers hate it). You can divide by an irrational number just as well as any other number. I wonder if this is a "rule" that was invented by math teachers from a time when calculators weren't so ubiquitous.

[duggydugg]

drop the 'go ahead and' expression

[dough]

A lot of borderline students will thank you because you explained that 1 + 2 = 3 sixteen different ways and they finally got it! That makes you feel good! But your more advanced students got bored and started acting up in class and got kicked out of school! Does that make you feel good, too??

[mikecarney]

I did it converting the fractions to decimals because I think in decimals and not complex fractions. You have the sq root of (4/7 X 14/3) or sq root of (.571 X 4.666) or sq root of 2.665 which is 1.63. 2 times the sq root of 6 divided by 3, to me, the problem is not completely solved yet.

[Gate_Seven]

(4/7=0, 57) (14/3=4, 66) —> 0, 57*4, 66=2, 66 —> SQ 2, 66= 1, 63

[Astrobrant]

I factored out the 4 after reducing and got 2√2/3. What's wrong with that? In addition to not allowing a radical in the denominator, is there another rule that you can't have a fraction in the radical?

[angusmcpherson]

I found that the sq rt of 2/3 × 2 has the same value on my calculator as 2 × sq rt of 6 ÷ 3, so, apparently, the calculator allows irrational numbers in the denominator of a radical.

[ericlipps]

2 square root (2/3). Factor out a square root of 4 to get 2 outside the radical, which is now to be multiplied by the square root of ((1*14)/(3*7)-->square root (14/21 = 2/3).

[njr]

Four minutes in and you still haven't started to simplify. Get to the point already!

Correction: five minutes in and you still haven't started to simplify...

[thecalculator]

Doesn't everybody recognize that "simplicity" is in the eye of the beholder. Somebody says that you can't have a square root n the denominator when a square root in the numerator is fine! Somehow, all the intermediate steps are NOT the right answer, but nothing at all would keep someone from taking the simple answer here and doing further manipulations. Then who decides which is "simpler".
The real math comes in the entirely unproved statement at the 8:26 minute point that Root(8/3) = Root(8) divided by Root(3). How can a teacher convince a ninth grader of that?