can someone please explain to me where my teacher got 36 from and why he canceled out the 4 and the 2 and the?

Question

2 and the 6?

how do you know when to cancel out a number?why?

http://i66.photobucket.com/albums/h267/irvingtons_girl_power/radical.jpg

Answer 1

4√5 / 3√8 x √8 /√8 =

4√40 /3 √64 =

4√40 / 3(8) =

4√40 / 24 = simplify the numerator 4 and the denominator 24. common factor is 4

√40 / 6 =

√4 √10 / 6 =

2 √10 / 6 = . . simplify the numerator 2 and the denominator 6. the common factor is 2

√10 / 3

The answer is √10/ 3

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Checking your answer when your teacher simplified 4√40 / 24 . the teacher did not reduce the numerator and denominator fully. it should have read √40 / 6.

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Answer 2

OK...I figured it out...the answer should be rad10/3, not 10/3. And there should be an equal sign in the middle between the 4rad40/24 and the 2rad10/36.

In the 2nd equation, the 4 is canceled by the 24 leaving rad40/6. Then factor out rad4=2 and cancel the 2 with the 6 leaves rad10/3.

Answer 3

Let's start right from the beginning.

[4sqrt(5)] / [3sqrt(8)]

To rationalize the denominator, multiply top and bottom by sqrt(8). This will give us

[4sqrt(5)sqrt(8)] / [3sqrt(8)sqrt(8)]

Note that sqrt(8) times itself will eliminate the square root, giving us just 8. Changing this accordingly,

[4sqrt(5)sqrt(8)] / [3(8)]

Simplifying,

[4sqrt(5)sqrt(8)] / [24]

Note that the 4 and the 24 will cancel as a 1 and a 6, giving us

sqrt(5)sqrt(8) / 6

We can combine the two square roots together by multiplying their insides. The square root of 5 times the square root of 8 is equal to the square root of 40.

sqrt(40) / 6

Note that we can simplify sqrt(40) as sqrt(4)sqrt(10)

sqrt(4)sqrt(10) / 6

But we know what the square root of 4 is; it's equal to 2.

2sqrt(10) / 6

Now we can cancel the 2 with the 6, leaving us with 3 on the bottom.

sqrt(10) / 3

It shouldn't simplify more than this. Either the teacher forgot to put the square root, or you did.

Answer 4

First of all, the answer is wrong. It should be (sqrt.10) / 3.
Now, start with the original fraction: [4*(sqrt.5)] / [3*(sqrt8)].
You can't have a sqrt. in the denominator, so multiply the equation by (sqrt.8) / (sqrt.8). Simplify that to get
[4*(sqrt.40)] / 24. You can simplify 4*(sqrt.40) to 8*(sqrt.10), since 2*2*2*5=40 (take out one set of 2's and multiply 4 by 2. leave the 2*5, or 10 under the radical.). So now we have
[8*(sqrt.10)] / 24. Divide 8 by 24 to get (sqrt. 10) / 3.

Answer 5

Some teachers have to explain to their students better in their classes.