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Maths year 11

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Original post by RDKGames
Remember your surd rules for multiplication and have a go. a⋅b=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{ab} use this for the first one to try and get the answer of 4.


How's this?



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Correct. Simplify it further.
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Reply 1303
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Original post by RDKGames
Correct. Simplify it further.




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Original post by z_o_e


I don't understand how you go from 242\sqrt4 to 222\sqrt2. Explain your thought process here.
Reply 1305
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Original post by RDKGames
I don't understand how you go from 242\sqrt4 to 222\sqrt2. Explain your thought process here.


Well I found what makes 4 and 2*2 makes four.

Surd 2 and surd 2 cancels out and gives 2 so we can put that two as it's simplified inside the surd.

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Original post by z_o_e
Well I found what makes 4 and 2*2 makes four.

Surd 2 and surd 2 cancels out and gives 2 so we can put that two as it's simplified inside the surd.

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Nope. Root 2 and root 2 cancel to give 2, yes you're right, but you took the square root of 4 in the first place, the root is now gone as it cancels with the 2's, so where are you getting another root from that makes you put the 2 inside it?
Reply 1307
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Original post by RDKGames
Nope. Root 2 and root 2 cancel to give 2, yes you're right, but you took the square root of 4 in the first place, the root is now gone as it cancels with the 2's, so where are you getting another root from that makes you put the 2 inside it?


I'm really not sure.
I have never covered surds. :/

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Original post by z_o_e
I'm really not sure.
I have never covered surds. :/

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Well that explains it. Watch this video to get the basics: https://www.youtube.com/watch?v=xpGlbt7Wg2U

The one thing that the video doesn't explain is what a surd is by definition. A surd is an irrational number you get when you take the root an integer. This also means that surds cannot be expressed as fractions.
(edited 7 years ago)
Reply 1309
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Original post by RDKGames
Well that explains it. Watch this video to get the basics: https://www.youtube.com/watch?v=xpGlbt7Wg2U

The one thing that the video doesn't explain is what a surd is by definition. A surd is an irrational number you get when you take the root an integer. This also means that surds cannot be expressed as fractions.


Yep I took a look at it and that's the area simplifying which I don't understand :frown:

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Original post by z_o_e
Yep I took a look at it and that's the area simplifying which I don't understand :frown:

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Give me an example from the video you don't understand and I'll walk you through it.
Reply 1311
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Original post by RDKGames
Give me an example from the video you don't understand and I'll walk you through it.


Yep I'm watching a video from maths solutions now.

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Reply 1312
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Original post by RDKGames
Give me an example from the video you don't understand and I'll walk you through it.


I think you need to explain this


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Original post by z_o_e
I think you need to explain this


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Okay there are several ways to think about it:

One way
If you list your square numbers from 1-10, you would get this:
12=1[br]22=4[br]32=9[br]42=16[br]52=25[br]62=36[br]72=49[br]82=64[br]92=81[br]102=1001^2=1[br]2^2=4[br]3^2=9[br]4^2=16[br]5^2=25[br]6^2=36[br]7^2=49[br]8^2=64[br]9^2=81[br]10^2=100

As you can see, you have 52=255^2=25 in there which means that 25 is a square number. If you were to square root both sides (which is the reverse of squaring a number) you would get 5=255=\sqrt{25}

Another way to think about it
When you have a square root of a number, it is the same as raising that number to the power of 1/2. From this we can manipulate it using laws of indices and surd multiplication rule like so:

25=5⋅5=5⋅5=51/2⋅51/2=(51/2)2=52/2=51=5\sqrt{25}=\sqrt{5\cdot 5}=\sqrt5 \cdot \sqrt5 = 5^{1/2} \cdot 5^{1/2} = (5^{1/2})^2 = 5^{2/2} = 5^1 = 5
(edited 7 years ago)
Reply 1314
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Original post by RDKGames
Okay there are several ways to think about it:

One way
If you list your square numbers from 1-10, you would get this:
12=1[br]22=4[br]32=9[br]42=16[br]52=25[br]62=36[br]72=49[br]82=64[br]92=81[br]102=1001^2=1[br]2^2=4[br]3^2=9[br]4^2=16[br]5^2=25[br]6^2=36[br]7^2=49[br]8^2=64[br]9^2=81[br]10^2=100

As you can see, you have 52=255^2=25 in there which means that 25 is a square number. If you were to square root both sides (which is the reverse of squaring a number) you would get 5=255=\sqrt{25}

Another way to think about it
When you have a square root of a number, it is the same as raising that number to the power of 1/2. From this we can manipulate it using laws of indices and surd multiplication rule like so:

25=5⋅5=5⋅5=51/2⋅51/2=(51/2)2=52/2=51=5\sqrt{25}=\sqrt{5\cdot 5}=\sqrt5 \cdot \sqrt5 = 5^{1/2} \cdot 5^{1/2} = (5^{1/2})^2 = 5^{2/2} = 5^1 = 5


So where does the 12 go?


So can we only simplify square numbers?


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Original post by z_o_e
So where does the 12 go?


So can we only simplify square numbers?


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That example was only for the root. After you simplify the root, and in this case you know that 25=5\sqrt{25}=5, you can replace the 25\sqrt{25} by 5.

So you would go from 12(25)12(\sqrt{25}) to 12(5)12(5)

(You can simplify non-squares too... don't get confused.)
Reply 1316
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Original post by RDKGames
That example was only for the root. After you simplify the root, and in this case you know that 25=5\sqrt{25}=5, you can replace the 25\sqrt{25} by 5.

So you would go from 12(25)12(\sqrt{25}) to 12(5)12(5)

(You can simplify non-squares too... don't get confused.)


For this question I got...

The one on the white board is my Final answer after looking at your examples of simplifying. ..


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Original post by z_o_e
For this question I got...

The one on the white board is my Final answer after looking at your examples of simplifying. ..


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Yep, your surd manipulation looks solid now. However, one slight error you might've missed, 37+37≠573\sqrt7 + 3\sqrt7 \not= 5\sqrt7 check that addition again. (also you can add 63 and 1, no point leaving them separate)
Reply 1318
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Original post by RDKGames
Yep, your surd manipulation looks solid now. However, one slight error you might've missed, 37+37≠573\sqrt7 + 3\sqrt7 \not= 5\sqrt7 check that addition again. (also you can add 63 and 1, no point leaving them separate)




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Reply 1319
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z_o_e
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Original post by RDKGames
Yep, your surd manipulation looks solid now. However, one slight error you might've missed, 37+37≠573\sqrt7 + 3\sqrt7 \not= 5\sqrt7 check that addition again. (also you can add 63 and 1, no point leaving them separate)


How did this go?

Shall I added 5 root 4 & root 6?



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