Re-write it with a root. If the power of the expression is less than 1, for example x1/3, the expression could be rewritten as cube root of x.
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In general, not usually.The square root of an irrational number is always irrational.The square root of a rational number is usually irrational, but not always. You can tell by this test:If both the numerator and denominator of the number expressed as a simplified fraction are perfect square numbers (a number whose square root is a whole number), then the square root of the whole fraction will be rational.Example: Sqrt(4) =2 (the positive one). Sqrt(1) = 1. Both are perfect squares.So sqrt(1/4) = sqrt(1)/sqrt(4) = 1/2. Another one: sqrt(4/9) = 2/3.
also -1
The number 27 has a cube root of 3, which is 2 (the smallest prime) plus 1.
-21 + 1.7320508i1 - 1.7320508i
[-1+sqrt(3)]1/4
You do. The other two are complex numbers, of interest only tomathematicians and engineers, and usually not listed.For example, the three cube roots of 8 are:2-1 + i sqrt(3)-1 - i sqrt(3)
Re-write it with a root. If the power of the expression is less than 1, for example x1/3, the expression could be rewritten as cube root of x.
It is easier to describe using an actual example. Say you have an expression x/sqrt(2). Then multiply by sqrt(2)/sqrt(2) (which is of course equal to 1 and we know that anything multiplied by 1 stays the same. This will get rid of the radical on the bottom. So the expression becomes x/sqrt(2) * sqrt(2)/sqrt(2) = [x*sqrt(2)]/2 where * means multiply
YES!!!! sqrt(x) = x^(0.5) = x^(1/2) It is just mathematical convenience, which expression you choose. NB Cube Root curt(x) = x^(0.333....) = x^(1/3) Fourth root 4rt(x) = x^(0.25) = x^(1/4) et.seq.,
Yes, but it involves the square root of -1. sqrt (-X) = sqrt (X) * sqrt(-1)
-1X-1X-1=-1 therefore cube root of -1 = -1
It will depend on where you put your parentheses. Root 7 -( 1/root 7) is different from (root 7-1)/root 7. * * * * * True, but a more helpful answer: [sqrt(7) - 1]/[sqrt(7) + 1] - [sqrt(7) + 1]/[sqrt(7) - 1] Multiplying the numerator and denominator of the first fraction by [sqrt(7) - 1] and the second fraction by [sqrt(7) + 1] = [sqrt(7) - 1]2/[7 - 1] - [sqrt(7) + 1]2/[7 - 1] =[7 - 2*sqrt(7) + 1]/6 - [7 + 2*sqrt(7) + 1]/6 = 16/6 = 8/3
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It is sqrt(3)*[1 + sqrt(2)]/3 or [1 + sqrt(2)]/sqrt(3)
Sqrt(001) = sqrt(1) = ±1