(The square root of 8 plus 1) divided by the square root of 8 =? Basic Algebra!

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[Dr_piFrog]

Congratulations -- you made a simple process very complicated. ----> (4 + sqrt(2))/4

[markmauldin]

You made this more complicated than necessary. An equally valid answer is 1 + 1/2*sqrt (2) and you can get there in 3 steps
(Sqrt(8) +1)/sqrt (8) = sqrt (8)/sqrt(8) + 1/sqrt(8)

Simplifying you get

1 + 1/sqrt(8) = 1 + 1/2sqrt(2)

[UnderAttack-xs]

I really enjoy your videos and your explanations. I kick off trolls who aren't nice, just saying.

These videos helped me a lot and thank you. Ignore the critics - these are awesome 👍

[ricardomccloskey]

no wonder so many people don't like math....if you need help falling asleep, this is a good vid to watch...

[dougnettleton]

If this is the correct answer, I would suggest the question should be: "Can you simplify to a common rational denominator?" I'm not sure how either the answer given or
1 + sqrt(2) / 4 "solves" the problem.

[Shay-qu]

Rewrite:
(8 ^ 1/2) / (8 ^ 1/2) + (1) / (8 ^ 1/2) .
The first set Cancels out Leaving 1 + (1/8 ^ 1/2)

We have a root in the denominator so we multiply the top and bottom by it:
1 + (1 * 8^ 1/2) divided by (8 ^ 1/2)²
1 + 2(2^1/2) / 8

The 1 is NOT affected by the denominator AND we can reduce the second part:
1 + (2^1/2) divided by 4

Technically the answer the professor gave is correct, BUT some (teachers like me) would mark that wrong because it wasn't FULLY reduced.

When you have a fraction as an exponent the numerator is a power and the denominator is the root. Also Remember the rule (x + y ) divided by (x) is the same as x divided by x + y divided by x. This is valid since both parts of the numerator are affected by the denominator.

Super simple and any of my passing 8th grade students would be able to solve this before going on Christmas break.

[delilahscott]

It doesn't require an 18 minute explanation !

[DanSpeed]

Thank you. I home school my son, so I love to keep up with my Math Skills. I keep telling him that math in our language is known as " Mathafu" which deriveds from the word "Ma" meaning truth. This is commom in Bantu. It all comes from ancient Kemet, when the Atlantians, Tehuti and the rest of them arrived to teach the Kemites the truths and universal laws of the universe.

[garyalabama]

I would have separated the numerator into two terms rationalizing the second term and left the answer as 1+ (sqrt(2)/4).

[silverhammer]

When you say, "Can you solve?, " that means, "What is the numerical value of this expression?" In this case, it is 1.3536. The question should be, "Can you reduce this expression?" For some reason, the presenter has an obsessive attachment to the idea that no expression should have a radical in the denominator. It's almost as bad as his near obsession with PEMDAS. In the Real World, where we want to see numbers, it makes absolutely no difference if there is a radical in the denominator or not.

[jimbuchanan]

How about 1 + (square root of 2 ) divided by 4 ???

[gavindeane]

Whilst it is true that (√8+1)/√8 is the same as (4+√2)/4, the idea that the first one is a question and the second one is the answer is just silly.

[yusrnm]

...Which is (sqrt(8)+1)/sqrt(8), which evaluates to approximately 1.353553. Either form, or even 1+sqrt(2)/4, can be crunched to approximately 1.353553 equally as easily.

[luizmorais]

Perfect!
If I'm going in a shop to buy some tiles for my bathroom, the seller ask me "how many sqt do you need?" Obviously I'll answer 4+root os 2 divided by 4! It's super usefull and effective!

[mr.mxyzptlks]

Multiply top and bottom by sqrt(8). Get 8 as the denominator (rationalize 🤓), multiply out the nominator to 8 + sqrt(8), and go from there. Not yet watched the vid, but I feel a bit more can be done. However, for the purpose of the exercise, I guess, the denominator, I’d give at least 80% credit at this stage 😎

[Don.Franco_Film]

Seems far simpler and clearer to just start with breaking the expression into the sum of 2 fractions
√8/√8 + 1/√8, which is (1 + 1/√8)

and then simplify to 1 + √2/4

[BluesChoker]

There was a lot of discussion about what algebraic rules could be used in solving this problem.The most common questions concerned dividing the numerator sqrt(8) by the denominator sqrt(8).

You can solve the problem this way, but must realize that this single fraction is the combined result of two fractions separate fractions—each with the common denominator of the sqrt(8).

So, the combined fraction must be expanded back to the original rational terms with the correct radical terms. This will also ensure that the denominator is rationalized (note that the sqrt(8) in the original equation is not rationalized because its solution include the term sqrt(2).

Here’s the solution version that divides the sqrt(8) by the sqrt(8). Just be aware of the rules and it’s easy:

1. Expand the fraction using its common denominator of sqrt(8):

Sqrt(8) 1
———— + ————
Sqrt(8) Sqrt(8)

2. Now simplify the two fractions:
1
1 + -———
Sqrt(8)

3. Simplify the Sqrt(8):

1
1 +. —————
2*sqrt(2)

4. Simplify by multiplying by one, in this case the Sqrt(2) / sqrt(2):

1 1 Sqrt(2)
+ ————. * ————-
2*sqrt(2). Sqrt(2)

5. Eliminate or combine terms:

1 Sqrt(2)
—- + —————————-
2*sqrt(2)*sqrt(2)
(2 * 2 = 4)

6. Combine to one fraction using the new common denominator of 4:

(4) Sqrt(2)
——— + ————
(4) 4

7. Solution: a new common, rationalized denominator of 4. We followed algebraic rules that allowed us to divide the sqrt(8) into itself.

4 + Sqrt(2)
————————
4

Regards,
Eric

[swdetroiter]

(4+ sqrt 2)/4 is not finished.

By partial fraction decomposition it becomes 1 + (1/(2* sqrt 2)).

Like this.

Sqrt 8= 2 * sqrt 2.

((2 * sqrt 2)+1)/(2* sqrt 2)

Decompose, the 2 sqrt 2's cancel,

Leaving (1 + (1/(2*sqrt 2))

[gibbogle]

Simplify, not solve (in the title) please.

[paulromsky]

Gave you a like. What's crazy about Algrebra, you can start off reducing something, but it could be out of order. For example, suppose you decided to reduce both of the sqrt(8) to 2*sqrt(2) first. That is not the right way to solve this but it is a valid algebraic method. In this case it won't be a problem, but in many cases doing something in the wrong order may give you the wrong answer or "stump" you. Yes, memory tricks like PEMDAS, FOIL, SOHCAHTOA are there for simple things, but there are no memory tricks to take any equation and in what order do the "multitude" of things in your "bag of tricks" to reduce or solve it. I aced but didn't retain things (swiss cheese) over the years... miss just one of the multitudes of rules and/or miss when to do them and... bingo... error/frustration. Algrebra makes sense to me, but there is just soooo many rules that fade with time (unless you are a mathematician). One would think there could be a single "algorithmic" approach to work any equation, but I started to try that and it was mess. So, sadly, you have get a "feel" on how how to solve something.... and to say I've seen this before - which would require you to do algebra virtually all day long 24/7 for your whole life. And Calculus even adds more rules and ordering. But people score well on the math in SATs becuse all the practice questions used in study guides and SAT prep classes are centered on identifying the "types" of problems and being prepared to solve only those... you've seen that before in study. You can get Ds in Algrebra, but study only the types used on SATs and you can do well.

I solved my dilemma by buying a TI-92+ calculator that solves algebra and calculus problems using symbology just like we use in math ("pretty print" as they call it).

There has to be a better way to burn EVERY rule and order into the brain... to be flawless in math, you MUST know it all COLD... else you get wrong answers and then what is the point.