here is a problem I am having, you must write the radical in its simpliest form, ...........................................please explain how to do the steps please..........................................
√2^10
the answer is 32
you help is greatly appreciated
2007-05-13 09:23:45 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
sitting here still confused
2007-05-13 09:29:59 · update #1
√2^10=(2^0.5)^10 (square root is power half)
............= 2^5 (rule of multiplying powers)
............= 32
2007-05-13 09:27:40 · answer #1 · answered by joncummins1968 4 · 0⤊ 0⤋
You have a bunch of correct answers. Here is why they're correct
A number expressed as m^n means m x m x m x ... x m for n factors... if n is a positive integer.
If n is a negative integer then it means the product of n factors of the reciprocal of number, m^(-n) means (1/m) x (1/m) x .... x (1/m) for n factors.
If n is a fraction , numerator of the fraction indicates the power (just as would any positive or negative integer), and the denominator of the fraction indicates the root of the number. For example, m^(1/n) means the nth root of m, or that number that, when used as a factor n times produces m. Thus m^(1/2) is the square root of m, so 4^(1/2) = 2.
Now (m^n)^p = m(np)
â2is the same as 2^(1.2)
(â2)^10, then is [2^(1.2)]^10
= 2^[(10)(1/2)] = 2^5
That's why people come up with 2^=32
2007-05-13 16:53:42 · answer #2 · answered by gugliamo00 7 · 0⤊ 0⤋
You can write â2 = 2^(1/2)
So [ 2^(1/2) ] ^ 10 = 2^(1/2 * 10)
= 2^5 = 32
2007-05-13 16:36:55 · answer #3 · answered by Dr D 7 · 0⤊ 0⤋
when you take the square root of 2^10 you get 2^5 (same rules as power taken to a power, you multiply, and square root is 1/2 power). 2^5 = 2 x 2 x 2 x 2 x 2 = 32.
2007-05-13 16:28:08 · answer #4 · answered by nimble_rabit 1 · 0⤊ 0⤋
â2^10
= (â2²)^5
= 2^5
=32
2007-05-13 17:45:44 · answer #5 · answered by Kathleen K 7 · 0⤊ 0⤋
You can break this down a number of ways:
â(2^10) =
â(2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2) =
â(4 * 4 * 4 * 4 * 4) =
â4 * â4 * â4 * â4 * â4 =
2 * 2 * 2 * 2 * 2 =
32
(â2)^10 =
(â2) * (â2) * (â2) * (â2) * (â2) * (â2) * (â2) * (â2) * (â2) * (â2) =
Grouping,
((â2) * (â2)) * ((â2) * (â2)) * ((â2) * (â2)) * ((â2) * (â2)) * ((â2) * (â2)) =
2 * 2 * 2 * 2 * 2 =
32
2007-05-13 17:05:25 · answer #6 · answered by Helmut 7 · 0⤊ 0⤋
â2^10
= â2.â2.â2.â2.â2.â2.â2.â2.â2.â2 where . is multiply
= 2 . 2 . 2 . 2 . 2
= 32
2007-05-13 16:41:10 · answer #7 · answered by fred 5 · 0⤊ 0⤋
â2^10=â(2^5)^2=2^5=32 answer
2007-05-13 16:29:43 · answer #8 · answered by Anonymous · 0⤊ 0⤋
just do that
2*2*2*2*2*2*2*2*2*2 = 1024
and then sqrt(1024) = 32
where is the problem?
2007-05-13 16:27:55 · answer #9 · answered by vale l 3 · 0⤊ 0⤋