1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
grandymaker [24]
2 years ago
6

Find the square roots by division method of 210,681 please tell me

Mathematics
1 answer:
padilas [110]2 years ago
8 0

Answer:

  459

Step-by-step explanation:

The "long division method" algorithm for square root makes use of the relation described by the square of a binomial.

  (a +b)² = a² +2ab +b² = a² +b(2a +b)

<h3>Steps</h3>

The value for which the root is desired is written with digits marked off in pairs either side of the decimal point.

The initial digit of the root is the integer part of the square root of the most-significant pair. Here that is floor(√21) = 4. This is shown in the "quotient" spot above the leftmost pair. The square of this value is subtracted, and the next pair brought down for consideration. Here, that means the next "dividend" is 506.

The next "divisor" will be 2 times the "quotient" so far, with space left for a least-significant digit. Here, that means 506 will be divided by 80 + some digits. As in regular long division, determining the missing digit involves a certain amount of "guess and check." We find that the greatest value 'b' that will give b(80+b) ≤ 506 is b=5. This is the next "quotient" digit and is placed above the "dividend" pair 06. The product 5(85) = 425 is subtracted from 506, and the next "dividend" pair is appended to the result. This makes the next "dividend" equal to 8181.

As in the previous step, the next "divisor is 2 times the quotient so far: 2×45 = 90, with space left for the least significant digit. 8181 will be divided by 900-something with a "quotient" of 9. So, we subtract the product 9(909) = 8181 from the "dividend" 8181 to get the next "dividend." That result is zero, so we're finished.

The root found here is 459.

__

<em>Additional comment</em>

In practice, roots are often computed using iterative methods, with some function providing a "starter value" for the iteration. Some iterative methods can nearly double the number of good significant digits in the root at each iteration.

Using this "long division method," each "iteration" adds a single significant digit to the root. Its advantage is that it always works, and is generally suitable for finding roots by hand. Once the number of root digits begins to get large, the "divisor" starts to be unwieldy.

You might be interested in
Alex has x number of baseball cards Danny has 10 more baseball cards than Alex how many baseball cards does Danny have:write you
Vilka [71]

Answer:

x+10

Danny has 10 + x baseball cards

7 0
3 years ago
399,713 rounded to nearest thousand
mina [271]
399,713 rounded to the nearest thousand is 400,000
3 0
3 years ago
State whether or not the following triangles are similar. If not, explain why not. If so, write a similarity statement
valentinak56 [21]

9514 1404 393

Answer:

  a) ∆RLG ~ ∆NCP; SF: 3/2 (smaller to larger)

  b) no; different angles

Step-by-step explanation:

a) The triangles will be similar if their angles are congruent. The scale factor will be the ratio of any side to its corresponding side.

The third angle in ∆RLG is 180° -79° -67° = 34°. So, the two angles 34° and 67° in ∆RLG match the corresponding angles in ∆NCP. The triangles are similar by the AA postulate.

Working clockwise around each figure, the sequence of angles from lower left is 34°, 79°, 67°. So, we can write the similarity statement by naming the vertices in the same order: ∆RLG ~ ∆NCP.

The scale factor relating the second triangle to the first is ...

  NC/RL = 45/30 = 3/2

__

b) In order for the angles of one triangle to be congruent to the angles of the other triangle, at least one member of a list of two of the angles must match for the two triangles. Neither of the numbers 57°, 85° match either of the numbers 38°, 54°, so we know the two triangles have different angle measures. They cannot be similar.

7 0
3 years ago
A Pest control company sprays insecticide around the perimeter of a 180 ft by 180 ft building. If the spray costs $.11 per foot,
andreev551 [17]
P = 4a.....this is the perimeter of a square
P = 4(180)
P = 720 ft

and if the spray cost 0.11 per ft......720 * 0.11 = 79.20 rounded to the nearest dollar is $ 79 <==
5 0
3 years ago
The sum of two numbers is 51 and the greater number is twice the smaller number. Find the numbers. a) set up the variables Let _
Gelneren [198K]

Answer:

  • 34 and 17

Step-by-step explanation:

a) set up the variables

Let x represent the first number Then  y will represent the second number.

b) What is the equation that represents the above situation?

  • x = 2y
  • x + y = 51

c) Solve the equation.

<u>Substitute x in the second equation and solve for y:</u>

  • x + y = 51
  • 2y + y = 51
  • 3y = 51
  • y = 51/3
  • y = 17

<u>Then find x</u>

  • x = 2y = 2*17 = 34
4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the integers: the sum of the three is 21 more than 2 times the smallest
    8·1 answer
  • How do you solve x+1/2x+4+4x
    13·2 answers
  • If 8 students have to split 5 pieces of cake how much did each student get?
    6·2 answers
  • The integer -3 would BEST represent which of these events?
    13·2 answers
  • Cos(x)^3-cos(2*x)+cos(x) = 0
    9·1 answer
  • One large bubble separates into four small bubbles so that the total area of the small bubbles is equal to the area of the large
    14·1 answer
  • Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the<br> number.
    8·1 answer
  • Find the missing value given the points and slope.<br><br><br>(x,1) and(4,6)<br><br><br> m=−5
    6·2 answers
  • Help!! <br> I need the answers ASAP
    14·1 answer
  • Select all of the potential solution(s) of the equation 2log5x = log54.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!