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Help with changing numbers into surds

I basically have R to the power of 6 = 1/8

I need to rewrite this in order to get 1/root 2 can anyone help get me started?
Reply 1
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Zacken
22
Original post by SunDun111
I basically have R to the power of 6 = 1/8

I need to rewrite this in order to get 1/root 2 can anyone help get me started?


R6=18=123=1323=(12)3R^6 = \frac{1}{8} = \frac{1}{2^3} = \frac{1^3}{2^3} = \left(\frac{1}{2}\right)^3

Now you know that if you have an=ba^n =b then a=b1/na= b^{1/n}.

So here: R=((12)3)1/6\displaystyle R= \left(\left(\frac{1}{2}\right)^3\right)^{1/6}

And you also know that (an)m=anm\left(a^{n} \right)^m = a^{nm}. So what does the above line simplify to?
(edited 7 years ago)
Reply 2
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SunDun111
OP
11
Original post by Zacken
R6=18=123=1323=(12)3R^6 = \frac{1}{8} = \frac{1}{2^3} = \frac{1^3}{2^3} = \left(\frac{1}{2}\right)^3

Now you know that if you have an=ba^n =b then a=b1/na= b^{1/n}.

So here: R=((12)3)1/6\displaystyle R= \left(\left(\frac{1}{2}\right)^3\right)^{1/6}

And you also know that (an)m=anm(a^{n})^m = a^{nm}. So what does the above line simplify to?


doesnt the 1 to the power of 3 over 2 to the power of 3, dosent the 3's cancel out? when you divide ?
Reply 3
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Zacken
22
Original post by SunDun111
doesnt the 1 to the power of 3 over 2 to the power of 3, dosent the 3's cancel out? when you divide ?


No. 1323=18\frac{1^3}{2^3}= \frac{1}{8}
Reply 4
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SunDun111
OP
11
Original post by Zacken
No. 1323=18\frac{1^3}{2^3}= \frac{1}{8}


ok thanks so it becomes 1/4 and then i simplify the 4 to 2 root 2
Reply 5
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Zacken
22
Original post by SunDun111
ok thanks so it becomes 1/4 and then i simplify the 4 to 2 root 2


Not quite. Okay, let's look at it in a simpler way:

R6=18R^6 = \frac{1}{8} - step 1.

R=(18)1/6\displaystyle R = \left(\frac{1}{8}\right)^{1/6} - step 2 by using an=b⇒a=b1/na^n = b \Rightarrow a = b^{1/n}.

R=11/681/6\displaystyle R = \frac{1^{1/6}}{8^{1/6}} - step 3 by using (ab)n=anbn\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}

R=181/6\displaystyle R = \frac{1}{8^{1/6}} - step 4 by using 1n=11^n = 1.

8=238 = 2^3 - step 5

81/6=(23)1/68^{1/6} = \left(2^{3}\right)^{1/6} - step 6

81/6=23/68^{1/6} = 2^{3/6} - step 7 by using (an)m=amn(a^n)^m = a^{mn}

Can you take it from here, if there's an issue with anything, please bold the "step" that confuses you.

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