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lora16 [44]
3 years ago
5

How to get a square root of a given number​

Mathematics
2 answers:
bonufazy [111]3 years ago
8 0

Answer:

See below

Step-by-step explanation:

The square root of a number is defined as \pm y=\sqrt[2]{x} where (\pm y)^{2} gives the original number. For example, \sqrt{4}=\pm2 because 2^{2}=2*2=4 and (-2)^{2}=-2*-2=4.

nlexa [21]3 years ago
4 0

Example of Calculating Square Roots with Multiplication :

  • The square root of 9 is 3. The number 9 is an integer. This number comes from multiplying 3×3 which results in the number 9
  • The square root of 25 is 5. The number 25 is an integer. This number comes from multiplying 5×5 which results in the number 25
  • The square root of 81 is 9. The number 81 is an integer. This number comes from multiplying 9×9 which results in the number 81
  • The square root of 100 is 10. The number 100 is an integer. This number comes from multiplying 10×10 which results in the number 100

Example of Calculating Square Roots by Division

  • The square root of 4 is 2. The number that divides 4 is the number 2, like 4: 2 makes the number 2. It cannot be divided anymore and can be multiplied by itself.
  • The square root of 9 is 3. The number that divides 9 is the number 3, such as 9: 3 to produce the number 3. It cannot be divided anymore and can be multiplied by itself.
  • The square root of 25 is 5. A number that divides 25 is 5, as 25:5 makes 5. It is indivisible and can be multiplied by itself.
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Answer:

What are the answer choices?

Step-by-step explanation:

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3 years ago
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4 years ago
Which expression is a cube root of -1+i√3?
Tpy6a [65]

Answer:

<em>The correct option is C.</em>

Step-by-step explanation:

<u>Root Of Complex Numbers</u>

If a complex number is expressed in polar form as

Z=(r,\theta)

Then the cubic roots of Z are

\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)

\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)

\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)

We are given the complex number in rectangular components

Z=-1+i\sqrt{3}

Converting to polar form

r=\sqrt{(-1)^2+(\sqrt{3})^2}=2

\displaystyle tan\theta=\frac{\sqrt{3}}{-1}=-\sqrt{3}

It's located in the second quadrant, so

\theta=120^o

The number if polar form is

Z=(2,120^o)

Its cubic roots are

\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)

\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)

\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)

Converting the first solution to rectangular coordinates

z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)

The correct option is C.

8 0
4 years ago
NEED HELP ASAP WILL MARK BRAINLIEST!
viktelen [127]

Answer:

log_{b} (5b) = 2.609

Given that:

log_{b} (3) = 1.099

log_{b} (5) = 1.609

Evaluating with that:

\sf log_b (5b) = log_b\left(5\right)+log_b\left(b\right)

            = \sf 1.609 + 1

             = \sf 2.609

Rule Used:

\rm \log _a\left(xy\right)=\log _a\left(x\right)+\log _a\left(y\right)

4 0
2 years ago
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