# What is Root: Definition and 941 Discussions

In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They most often lie below the surface of the soil, but roots can also be aerial or aerating, that is, growing up above the ground or especially above water.

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### I Noise Proportional to Square Root of Illumination: Need Formula Help

Many people have said that the noise that affects laser light is proportional to the square root of the illumination. But I can't find the formula. Can anyone help?
2. ### Find the root of the given equation in terms of ##u##

Hmmmm was a nice one... took me some time to figure out ...seeking alternative ways ... My working; ##x=\dfrac{-2±\sqrt{4+4 \sinh^2 2u}}{2 \sinh 2u}## ##x=\dfrac{-2±2\sqrt{1+ \sinh^2 2u}}{2 \sinh 2u}## ##x=\dfrac{-1±\sqrt{1+ \sinh^2 2u}}{\sinh 2u}## ##x=\dfrac{-1+\sqrt{1+ \sinh^2 2u}}{\sinh...
3. ### Engineering Can I use root locus when the input is the negative feedback?

I have used root locus before but my confusion now is that the input is the negative feedback. Usually when I have negative feedback I consider the the error between the input (ideal) signal and the observed signal. Also, in this case what is the tranfer function since u = -k*y, and what does...
4. ### I Calculating the root of a number by hand

Hi, is it possible, is there any formula that can help me to take root from (for example) 1,2 without a calculator (by hand)? For example, there is a cos(x) formula that can be calculated on the paper: $$\cos x=\sum_{n=0}^{\infty}(-1)^{n} \frac{x^{2 n}}{(2 n) !}$$ There is the Babylonian method...
5. ### Finding square root of number i.e. ##\sqrt{\dfrac{16}{64}}##

The correct answer is; ##\sqrt{\dfrac{16}{64}}=\dfrac{4}{8}## . I do not seem to understand why some go ahead to simplify ##\dfrac{4}{8}## and getting ##\dfrac{1}{2}## which is clearly wrong. I do not know if any of you are experiencing this... I guess more emphasis on my part. Cheers! Your...
6. ### B Stumped by Math: Finding the Root of x^4

I feel incredibly stupid for not getting this. I found this math problem in the beginning of my precalculus book: 12√x^4 That's 12th root of x to the fourth power. How do I find the root of x if the root is larger than the exponent?
7. ### B Derivative of Square Root of x at 0

When you use the power rule to differentiate the square root, the result is 1/2(sqrt. x) which is undefined at 0. But, when you use the definition of the definition of the derivative to calculate it, the result is infinity. What causes this difference between these two methods?
8. ### B Square Root of an Odd Powered Integer is Always Irrational?

Is it always true that the square root of an odd powered integer will always be irrational?
9. ### Show that square root of 3 is an irrational number

##\sqrt{3}## is irrational. The negation of the statement is that ##\sqrt{3}## is rational. ##\sqrt{3}## is rational if there exist nonzero integers ##a## and ##b## such that ##\frac{a}{b}=\sqrt 3##. The fundamental theorem of arithmetic states that every integer is representable uniquely as a...
10. ### Repeated root in field of char 0

Proof: We will first show ##\gcd(p(x), p'(x)) = 1##. Define ##d(x) = \gcd(p(x), p'(x))##. Then we can find ##q(x) \in F[x]## such that ##p(x) = d(x)q(x)##. But ##p(x)## is irreducible which means ##d(x)## is constant or ##q(x)## is constant. If ##q(x)## is constant, then ##\deg d(x) = \deg...
11. ### I Is the odd root of an even number always an irrational number?

Is the odd root of an even number always an irrational number? For example the 7th root or the 11th root, etc. of an even number.
12. ### I Finding a polynomial that has solution (root) as the sum of roots

AIUI, an algebraic is defined as a number that can be the solution (root) of some integer polynomial, and is any number that can be constructed via any binary arithmetic operation or unary root operation with arguments that are themselves algebraic numbers. I have been able to prove this for...

33. ### B Principal square root of a complex number, why is it unique?

This is a quote from "Calculus", by Robert A. Adams. It's a translation from spanish: "Roots of square numbers If ##a## is a positive real number, there exist two different real numbers whose square is ##a##. They are ##\sqrt{a}\;## (the positive square root of ##a##) ##-\sqrt{a}\;## (the...
34. ### MHB Monotonically convergence to the root

Hey! 😊 We have the following iteration from Newton's method \begin{align*}x_{k+1}&=x_k-\frac{f(x_k)}{f'(x_k)}=x_k-\frac{x_k^n-a}{nx_k^{n-1}}=\frac{x_k\cdot nx_k^{n-1}-\left (x_k^n-a\right )}{nx_k^{n-1}}=\frac{ nx_k^{n}-x_k^n+a}{nx_k^{n-1}}\\ & =\frac{ (n-1)x_k^{n}+a}{nx_k^{n-1}}\end{align*} I...
35. ### Iterative root finding for the cube root of 17

Firstly, the cube root of 17 is 2.571281591 which is 2.57 to 3.s.f. Initially, I thought about just approaching this problem using the Newton-Raphson Method when x0=2. In which case; x^3=17 x^3-17=0 Using the Newton-Raphson iterative formula xn+1=xr-f(xn)/f’(xn) f(x)=x^3-17 f’(x)=3x^2...
36. ### Using Equipartition theory to solve the root mean square of a angle.

For the first question, i believe that mechanical energy is conserved hence we can derive the total energy i think. In regards to the second question, I'm assuming its at room temperature, so helium is monotonic therefore it has 3 degrees of freedom, therefore its internal energy is 3/2KT. I am...
37. ### Find the square root of a surd term

find the square root of ## a+b+√(2ab +b^2)## let ##√[a+b+√(2ab +b^2)]= ±(√x +√y)## then, ##a+b+√(2ab +b^2)= x+y+ 2√(xy)## where ##a+b=x+y##.......1 ##(b+a)^2-a^2=4xy## .....2 from 2, ##a^2=(b+a)^2-4xy## ##a=√[x+y)^2-4xy]## ##a=√[x^2-2xy+y^2]## ##a=x-y## therefore...
38. ### MHB How to Solve an Equation with Square Roots?

Please Help me solve it $\sqrt{x}+\sqrt{x+8}=8$ thanks
39. ### Root Mean Square Velocity of Gases

This question came in NEET Exam 2018.Now my first query is that in the question,the mass of one Oxygen molecule is given wrong.Its exactly half it's true value.I don't think anybody has noticed this before because I couldn't find any change in the printed question on so many different books...
40. ### A Integral of a sinc squared function over a square root function

I want to find the analytical solution to the integral given below. \int_{-\infty}^{\infty} \frac{ sinc^2(\frac{k_yb}{2})}{\sqrt{k^2 - k_x^2 - k_y^2}}dk_y In other words, \int_{-\infty}^{\infty} \frac{ \sin^2(\frac{k_yb}{2})}{(\frac{k_yb}{2})^2\sqrt{k^2 - k_x^2 - k_y^2}}dk_y Can this be...
41. ### B Is the sign of the square root dependent on the argument inside it?

Could it be said that since ##a=A(f(x))\sqrt{f(x)}##, with ##A(x)\in\{1,-1\}## then ##a^2=f(x)##,, that ##a## is the square root of ##f(x)## ? In other words could the sign of the root depend on the argument inside it ? Else it would have to be chosen by human free will and to be blocked for...
42. ### I Physical meaning of the highest root / weight

As some simple Lie groups and their algebras are essential for our current understanding of QM, I wondered if especially the highest positive (or likewise lowest negative) root can be explained physically. The roots are the weights of the adjoint representation. Are their physical meanings...
43. ### MHB Condition for A Quartic Equation to have a Real Root

Show $20a^2+20b^2+5c^2\ge 64$ if $y=x^4+ax^3+bx^2+cx+4$ has a real root.
44. ### MHB Complex Function Theory: Explaining Example 1.5, Section 1.2, Chapter III

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I have yet another question regarding Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...
45. ### MHB Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need further help with other aspects of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...
46. ### MHB Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need help with an aspect of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III, reads as...
47. ### MHB Verify Gamelin's Remark: Complex Square and Square Root Functions

I am reading Theodore W. Gamelin's book: "Complex Analysis" ... I am focused on Chapter 1: The Complex Plane and Elementary Functions ... I am currently reading Chapter 1, Section 4: The Square and Square Root Functions ... and need some help in verifying a remark by Gamelin ... ... The...
48. ### Cube root long division method

On the right paragraph it says "The trial divisor 1200 goes into the dividend 13952, 8 times" Clearly 1200 goes into 13952, 11 times. I don't understand why 8 is (arbitrarily?) chosen. Please help. Thanks.
49. ### Should the Dalvik cache on Android phones be cleared periodically?

Finally, after a lot of hesitation, I rooted my phone (Samsung Galaxy On7, Android 6.0.1) using Magisk systemless root. The main aim was to remove pre-installed useless software (often termed "bloatware"). I didn't want to flash Magisk using TWRP, because installing TWRP would remove the stock...
50. ### I How to know if a complex root is inside the unit circle

Hi. I have been trying to calculate the real definite integral with limits 2π and 0 of ## 1/(k+sin2θ) ## To avoid the denominator becoming zero I know this means |k|> 1 Making the substitution ##z= e^{iθ}## eventually ends up giving me a quadratic equation in ##z^2## with 2 pairs of roots...