#Radiciation #Squareroot #SquareRoot Property #SquareRootomPotency #Squareroot Exponent
Radiciation can be resolved by memorizing rules or understanding what it is. Radiciation is merely an exponent division.
For example, the square root of a number x is the same thing as that number x to the half. Normally square root doesn't put the number 2 in the root, but it's there, and since the number is raised to 1, the x gets raised to half.
For example the cube root of a number x is equal to x to the 1 divided by 3.
What if it's the fourth root? Same thing, only now divided by 4.
And now let's generalize? A root of the value a, of a number x to the b, is equal to the value x to the b divided by a.
Understanding this, we have the basis of all radiciation, remember it is necessary to understand basic exponentiation before seeing radiciation.
So, now let's understand the functioning of some rules of rooting, which usually have them memorized. But we're not going to do this:
Let the enzyme root of any number "a" and its set raised to the nth value, we have that the enzyme root of a is equal to "a" to the 1 divided by "n", when we have the power of a large number, we multiply the exponent of the number by the power of that number, generating the value "n" divided by "n", which is one, thus the value is the number "a".
Remember that if we understand it is much better for solving exercises than merely memorizing.
So let's do some exercises?
Let the fifth root of the number two be all raised to 5, we know that the radiciation is nothing more than the value of the root dividing into the power. And if we raise everything to the number 5, it's like we multiply the power by 5, as it has the value 5 dividing then we have the number raised to 1, which is itself.
Now, to make it a little more difficult, instead of having the "n" values equal, let's call one "p".
Remember that radiciation is the exponent with division. Following the same rules already seen, the "p" that is in the power, will multiply the exponent that is being divided by n.
We are now going to give values to the variables, that is, the letters p and n.
We have the root 14, of the number 7 everything to the 6. So the root 14, goes as a divisor exponent, so we have 7 to the 1 divided by 14, everything to the 6, then we multiply the 6 in the exponent, we have 7 to the 6 divided by 14, but we can simplify, 6 is twice 3, and 14 is twice 7, when we have two equal numbers, so when the dividend is equal to the divisor, the result is one. Thus, the result of the power is 3 divided by 7, if we want to go back to standard rooting, just put the value that divides as the rooting value, then we have the seventh root of seven to the third. As a connoisseur of practical Mathematics, the best value is 7 raised to 3 divided by 7.
Let's take a break, and we'll see more properties in the next video.
sqrt{x}=x^{frac{1}{2}}\
sqrt[2]{x^{1}}=sqrt{x}=x^{frac{1}{2}}\
sqrt[3]{x^{1}}=x^{frac{1}{3}}\
sqrt[3]{x^{4}}=x^{frac{1}{4}}\
sqrt[a]{x^{b}}=x^{frac{b}{a}}\
left (sqrt[n]{a}
ight )^{n}=left (a^{frac{1}{n}}
ight )^{n}=a^{frac{n} {n}}=a\
left (sqrt[5]{2}
ight )^{5}=left (2^{frac{1}{5}}
ight )^{5}=2^{frac{5} {5}}=2\
left (sqrt[n]{a}
ight )^{p}=left (a^{frac{1}{n}}
ight )^{p}=a^{frac{p} {n}}\
left (sqrt[14]{7}
ight )^{6}=left (7^{frac{1}{14}}
ight )^{6}=7^{frac{6} {14}}=7^{frac{2.3}{2.7}}=7^{frac{3}{7}}=sqrt[7]{7^{3}}\
