What does the small number on top of the square root symbol mean?
2 Apr 2025 at 5:06am
$\begingroup$ Minor point: I notice quite a few elementary algebra books as well as some writers here taking the view that the n-th root of x is defined as x to the power 1/n. I disagree strongly. I disagree strongly.
radicals - Square root of a number squared is equal to the absolute ...
1 Apr 2025 at 10:32pm
You are referring to the principal square root. From Wikipedia: "Although the principal square root of a positive number is only one of its two square roots, the designation 'the square root' is often used to refer to the principal square root."
What is $\\sqrt{i}$? - Mathematics Stack Exchange
31 Mar 2025 at 9:12am
The suaqre root of a (non-negative) real number is non-negative by definition, but is there a similar decision for "the" square root of other (complex) numbers? $\endgroup$ ? Wolfgang Kais Commented Jul 8, 2023 at 17:59
How do you find the square root of 361? + Example - Socratic
27 Mar 2025 at 10:35am
361 = 19^2, so sqrt(361) = 19. See explanation for a few methods... Prime Factorisation One of the best ways to attempt to find the square root of a whole number is to factor it into primes and identify pairs of identical factors. This is a bit tedious in the case of 361 as we shall see: Let's try each prime in turn: 2 : No: 361 is not even. 3 : No: The sum of the digits is not a multiple of 3 ...
inequality - Taking the square roots in inequalities - Mathematics ...
30 Mar 2025 at 1:59pm
I have a question regarding taking square roots in inequalities. I have a problem asking: Suppose $3x^2+bx+7>0$ for every real number x. Show that $|b|<2\\sqrt{21}$. In an earlier question i...
calculus - Definite Integral of square root of polynomial - Mathematics ...
29 Mar 2025 at 5:32am
I need to learn how to find the definite integral of the square root of a polynomial such as: $$\sqrt{36x + 1}$$ or $$\sqrt{2x^2 + 3x + 7} $$ EDIT: It's not guaranteed to be of the same form. It could be any polynomial that can't be easily factored into squares. This isn't homework, I'm studying for a final.
Find the square root of a matrix - Mathematics Stack Exchange
1 Apr 2025 at 9:42pm
As traditional known the square root of any number would have two result, its cube root would have three ...
How do you find the square root of #13#? - Socratic
26 Mar 2025 at 4:46am
Use a Newton Raphson method to find: sqrt(13) ~~ 842401/233640 ~~ 3.60555127547 Since 13 is a prime number, there is no simpler form for its square root. sqrt(13) is an irrational number somewhere between 3 = sqrt(9) and 4 = sqrt(16). Linearly interpolating, a reasonable first approximation would be: sqrt(13) ~~ 3.6 = 18/5 We can get better approximations from our initial one (call it a_0 ...
Approximating square roots using binomial expansion.
2 Apr 2025 at 12:55am
In fact you can take any two numbers which can be added to get 2 (not nesserly 0.01 but at least you should know the root of one of them So for example $\sqrt{2} = {(1+1)^{1/2}}$ Know all what you need is to expand it using bio theorem and for 2 terms you ll get 1.5
First Principles Example 3: square root of x - Calculus - Socratic
27 Mar 2025 at 8:34am
The derivative of \\sqrt{x} can also be found using first principles. Plugging \\sqrt{x} into the definition of the derivative, we multiply the numerator and denominator by the conjugate of the numerator, \\sqrt{x+h}+\\sqrt{x}. Simplifying and taking the limit, the derivative is found to be \\frac{1}{2\\sqrt{x}}.
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
2 Apr 2025 at 5:06am
$\begingroup$ Minor point: I notice quite a few elementary algebra books as well as some writers here taking the view that the n-th root of x is defined as x to the power 1/n. I disagree strongly. I disagree strongly.
radicals - Square root of a number squared is equal to the absolute ...
1 Apr 2025 at 10:32pm
You are referring to the principal square root. From Wikipedia: "Although the principal square root of a positive number is only one of its two square roots, the designation 'the square root' is often used to refer to the principal square root."
What is $\\sqrt{i}$? - Mathematics Stack Exchange
31 Mar 2025 at 9:12am
The suaqre root of a (non-negative) real number is non-negative by definition, but is there a similar decision for "the" square root of other (complex) numbers? $\endgroup$ ? Wolfgang Kais Commented Jul 8, 2023 at 17:59
How do you find the square root of 361? + Example - Socratic
27 Mar 2025 at 10:35am
361 = 19^2, so sqrt(361) = 19. See explanation for a few methods... Prime Factorisation One of the best ways to attempt to find the square root of a whole number is to factor it into primes and identify pairs of identical factors. This is a bit tedious in the case of 361 as we shall see: Let's try each prime in turn: 2 : No: 361 is not even. 3 : No: The sum of the digits is not a multiple of 3 ...
inequality - Taking the square roots in inequalities - Mathematics ...
30 Mar 2025 at 1:59pm
I have a question regarding taking square roots in inequalities. I have a problem asking: Suppose $3x^2+bx+7>0$ for every real number x. Show that $|b|<2\\sqrt{21}$. In an earlier question i...
calculus - Definite Integral of square root of polynomial - Mathematics ...
29 Mar 2025 at 5:32am
I need to learn how to find the definite integral of the square root of a polynomial such as: $$\sqrt{36x + 1}$$ or $$\sqrt{2x^2 + 3x + 7} $$ EDIT: It's not guaranteed to be of the same form. It could be any polynomial that can't be easily factored into squares. This isn't homework, I'm studying for a final.
Find the square root of a matrix - Mathematics Stack Exchange
1 Apr 2025 at 9:42pm
As traditional known the square root of any number would have two result, its cube root would have three ...
How do you find the square root of #13#? - Socratic
26 Mar 2025 at 4:46am
Use a Newton Raphson method to find: sqrt(13) ~~ 842401/233640 ~~ 3.60555127547 Since 13 is a prime number, there is no simpler form for its square root. sqrt(13) is an irrational number somewhere between 3 = sqrt(9) and 4 = sqrt(16). Linearly interpolating, a reasonable first approximation would be: sqrt(13) ~~ 3.6 = 18/5 We can get better approximations from our initial one (call it a_0 ...
Approximating square roots using binomial expansion.
2 Apr 2025 at 12:55am
In fact you can take any two numbers which can be added to get 2 (not nesserly 0.01 but at least you should know the root of one of them So for example $\sqrt{2} = {(1+1)^{1/2}}$ Know all what you need is to expand it using bio theorem and for 2 terms you ll get 1.5
First Principles Example 3: square root of x - Calculus - Socratic
27 Mar 2025 at 8:34am
The derivative of \\sqrt{x} can also be found using first principles. Plugging \\sqrt{x} into the definition of the derivative, we multiply the numerator and denominator by the conjugate of the numerator, \\sqrt{x+h}+\\sqrt{x}. Simplifying and taking the limit, the derivative is found to be \\frac{1}{2\\sqrt{x}}.
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
