[MOVED] simplifying square roots: factoring numbers

Do you understand that n<SUP>2</SUP>=(n)(n)?
Then n<SUP>3</SUP>=(n)(n)(n), right?
6<SUP>2</SUP>=(6)(6)=36, right.
Thus 36 is a perfect square.
{1,4,9,16,25,49,64,81} is the set of perfect squares less than 100.
But 100 is also a perfect square: (10)(10).
So you see 96 is not a perfect square.
There is no whole number such that (n)(n)=96.
The symbol \(\displaystyle \sqrt n\) stands for a real number such that \(\displaystyle \left( {\sqrt n } \right)^2 = n\).

You see the square root is ‘sort of the reverse’ of the square.
\(\displaystyle \sqrt 1 = 1,\quad \sqrt 4 = 2,\quad \sqrt {49} = 7,\quad \sqrt {64} = 8\)

But \(\displaystyle \sqrt {98}\) cannot equal a whole number because 98 is not a perfect square.

However, \(\displaystyle \sqrt {98} = \sqrt {2\left( {49} \right)} = \left( {\sqrt {49} } \right)\left( {\sqrt 2 } \right) = 7\sqrt 2 .\)

So we factor the number, find the greatest perfect square in it.
Say 108=(2)(58) but neither of those is a perfect square.
It is true that 108=(4)(27). Oh 4 is a perfect square.
BUT 108=(3)(36) and 36 is an even greater perfect square.
So \(\displaystyle \sqrt {108} = \sqrt {36} \sqrt 3 = 6\sqrt 3 .\)
 
Ok so 96 has no square?

I understand All this

Do you understand that n2=(n)(n)?
Then n3=(n)(n)(n), right?
62=(6)(6)=36, right.
Thus 36 is a perfect square.
{1,4,9,16,25,49,64,81} is the set of perfect squares less than 100.
But 100 is also a perfect square: (10)(10).
So you see 96 is not a perfect square.

But I dont understand the rest.
No worries ill figure it out sooner or later.

thanks for the help guys
 
Monkeyeatbutt said:
Ok so 96 has no square?
Click to expand...
The square of 96 is 96<sup>2</sup> = 9216. The square root of 96 is sqrt[96] = 4sqrt[6]. Which are you trying to find? Or, since both of these answers were provided earlier, are you actually trying to find the answer to something else?

Thank you.

Eliz.
 
Its the square root.

Maby im getting so confused because of so many things being explained. I have the answer Im sure I can figure out the rest from there.

A few more questions first though

When you simplify problems like squrt8 x squrt18 Do you mutply them together then solve or would the answer be the 2 numbers times eachother agin?

How would you simplify fractions? I have one thats squrt4/11

Well i had better do the rest of these Thanks a ton guys
 
Monkeyeatbutt said:
When you simplify problems like squrt8 x squrt18 Do you mutply them together then solve or would the answer be the 2 numbers times eachother agin?
Click to expand...
The answer will vary with the exercise in question. The expression could simplify to be one whole number:

. . . . .sqrt[2]sqrt[8] = sqrt[16] = 4

...one square root:

. . . . .sqrt[2]sqrt[3] = sqrt[6]

...or the product of a whole number and a root:

. . . . .sqrt[2]sqrt[10] = sqrt[20] = sqrt[4]sqrt[5] = 2sqrt[5]

Monkeyeatbutt said:
How would you simplify fractions? I have one thats squrt4/11
Click to expand...
I assume you mean "fractional expressions containing radicals"...? The answer, as above, will vary with the fractional expression in question.

For a complete explanation, try doing a search for lessons on simplifying radicals.

Eliz.
 
Hey. I think I know what you are trying to do:

\(\displaystyle \
\begin
\sqrt {96} = \sqrt (16 x 6) \
= 4\sqrt 6\\)

First find the HCF of the number under the square root and its partner and then write them under the square root. Then as you can find root 16 in your head it becomes 4 and you leave 6 under the root sign.

BTW why are you studying a maths course. Are you looking for a job that requires maths?
 
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