2736 squared, (2736)2, is the number you get when multiplying 2736 times 2736.It can also be looked at as exponentiation involving the base 2736 and the exponent 2.The term is usually pronounced two thousand seven hundred thirty-six times two thousand seven hundred thirty-six or two thousand seven hundred thirty-six squared.The square of 2736 is a perfect square because the number is the product of the two equal integers 2736.It can be written as 2736 × 2736 or in exponential form.Read on to learn everything about the number two thousand seven hundred thirty-six squared, including useful identities.
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On this Site You Can Learn all About Squared Numbers! Click To Tweet(2736)2 = 7,485,696
2736 × 2736 = 7,485,696
The inverse operation of squaring two thousand seven hundred thirty-six is extracting the square root of 2736, explained here.
In the next section we elaborate on what is 2736 squared and there you can also find our calculator.
What is 2736 Squared?
A square is a flat shape with four equal sides; every angle is 90°.Hence, a square with side length 2736 has an area of 7,485,696.2736 squared equals the sum of the first 2736 odd numbers:In addition, the number can be calculated from 2735 squared using the following identity:n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(2736)2 = 27352 + 2735 + 2736 = 27352 + 5471 = 7,485,696It can be also be computed from 2735 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(2736)2 = 2 x 27352 – 27342 + 2 = 2 x 7480225 – 7474756 + 2 = 7,485,696
The difference between the perfect square of 2736 and its predecessor, 2735, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 2736 – 1 = 5471 = (2736)2 – 27352 = 7,485,696 – 7480225 = 5471
2736 is even, and the square numbers of even numbers are also even: (2n)2 = 4n2.
Squares of even numbers like 2736 are divisible by 4 for= n2.If you want to calculate the square of any number, not only integers like 2736, you can use our calculator above.Enter your number; nothing else to be done.
A square similar to 2736 is, for example: square of 2738.
Ahead, we discuss the frequently asked questions.
FAQs About 2736 Squared
Click on the question which is of interest to you to see the collapsible content answer.The square of 2736 is 7,485,696.
2736 squared can be written as (2736)2 (a small 2 is placed to the top right of 2736) or 2736^2.
Yes, the square roots of 2736 are ±52.306787323.
The perfect square of 2736 is 2736 × 2736 = 7,485,696.
You square 2736 by multiplying 2736 by itself.
No, 2736 is the square of the irrational number 52.3067873225.
The square of negative 2736 is 7,485,696.
The following table contains the squares of numbers close to 2736.
Table
| 2731 | 7,458,361 |
| 2732 | 7,463,824 |
| 2733 | 7,469,289 |
| 2734 | 7,474,756 |
| 2735 | 7,480,225 |
| 2736 | 7,485,696 |
| 2737 | 7,491,169 |
| 2738 | 7,496,644 |
| 2739 | 7,502,121 |
| 2740 | 7,507,600 |
| 2741 | 7,513,081 |
Two Thousand Seven Hundred Thirty-Six Squared
By reading so far you know all about squaring the number 2736 and calculating it using recursive methods, or as sum, product or by exponentiation.2736 squared is equivalent to 7,485,696.If you were searching for what is 2736 squared in math or if you typed whats 2736 squared in the search engine you now have all the answers, too.
The same goes for searches like square2736, and 2736 to the 2nd power, just to name a few more examples people are often looking for.Note that you can also find many perfect squares including 2736 squared using the search form in the sidebar of this page.Ahead is the summary of our information.
Conclusion
To sum up,2736 squared = 2736 × 2736 = (2736)2 = 7,485,696.
The exponentiation form is mostly used to denote two thousand seven hundred thirty-six squared.If this article about the square of 2736 has been of help to you then please share it by means of the social buttons. And should you want to leave a comment related to 2736 squared use the form below.Websites which are related to this one can be found in the “recommended sites” section in the sidebar.Last, but not least, don’t forget to install our absolutely free PWA app (see menu or sidebar), or to bookmark us.And come back soon!Thanks for your visit.
121\times 1800=100\left(90+x\right)\left(30-x\right)
Multiply both sides of the equation by 36300, the least common multiple of 300,363.
217800=100\left(90+x\right)\left(30-x\right)
Multiply 121 and 1800 to get 217800.
217800=\left(9000+100x\right)\left(30-x\right)
Use the distributive property to multiply 100 by 90+x.
217800=270000-6000x-100x^{2}
Use the distributive property to multiply 9000+100x by 30-x and combine like terms.
270000-6000x-100x^{2}=217800
Swap sides so that all variable terms are on the left hand side.
270000-6000x-100x^{2}-217800=0
Subtract 217800 from both sides.
52200-6000x-100x^{2}=0
Subtract 217800 from 270000 to get 52200.
-100x^{2}-6000x+52200=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-6000\right)±\sqrt{\left(-6000\right)^{2}-4\left(-100\right)\times 52200}}{2\left(-100\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -100 for a, -6000 for b, and 52200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-6000\right)±\sqrt{36000000-4\left(-100\right)\times 52200}}{2\left(-100\right)}
Square -6000.
x=\frac{-\left(-6000\right)±\sqrt{36000000+400\times 52200}}{2\left(-100\right)}
Multiply -4 times -100.
x=\frac{-\left(-6000\right)±\sqrt{36000000+20880000}}{2\left(-100\right)}
Multiply 400 times 52200.
x=\frac{-\left(-6000\right)±\sqrt{56880000}}{2\left(-100\right)}
Add 36000000 to 20880000.
x=\frac{-\left(-6000\right)±600\sqrt{158}}{2\left(-100\right)}
Take the square root of 56880000.
x=\frac{6000±600\sqrt{158}}{2\left(-100\right)}
The opposite of -6000 is 6000.
x=\frac{6000±600\sqrt{158}}{-200}
Multiply 2 times -100.
x=\frac{600\sqrt{158}+6000}{-200}
Now solve the equation x=\frac{6000±600\sqrt{158}}{-200} when ± is plus. Add 6000 to 600\sqrt{158}.
x=-3\sqrt{158}-30
Divide 6000+600\sqrt{158} by -200.
x=\frac{6000-600\sqrt{158}}{-200}
Now solve the equation x=\frac{6000±600\sqrt{158}}{-200} when ± is minus. Subtract 600\sqrt{158} from 6000.
x=3\sqrt{158}-30
Divide 6000-600\sqrt{158} by -200.
x=-3\sqrt{158}-30 x=3\sqrt{158}-30
The equation is now solved.
121\times 1800=100\left(90+x\right)\left(30-x\right)
Multiply both sides of the equation by 36300, the least common multiple of 300,363.
217800=100\left(90+x\right)\left(30-x\right)
Multiply 121 and 1800 to get 217800.
217800=\left(9000+100x\right)\left(30-x\right)
Use the distributive property to multiply 100 by 90+x.
217800=270000-6000x-100x^{2}
Use the distributive property to multiply 9000+100x by 30-x and combine like terms.
270000-6000x-100x^{2}=217800
Swap sides so that all variable terms are on the left hand side.
-6000x-100x^{2}=217800-270000
Subtract 270000 from both sides.
-6000x-100x^{2}=-52200
Subtract 270000 from 217800 to get -52200.
-100x^{2}-6000x=-52200
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{-100x^{2}-6000x}{-100}=\frac{-52200}{-100}
Divide both sides by -100.
x^{2}+\frac{-6000}{-100}x=\frac{-52200}{-100}
Dividing by -100 undoes the multiplication by -100.
x^{2}+60x=\frac{-52200}{-100}
Divide -6000 by -100.
x^{2}+60x=522
Divide -52200 by -100.
x^{2}+60x+30^{2}=522+30^{2}
Divide 60, the coefficient of the x term, by 2 to get 30. Then add the square of 30 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+60x+900=522+900
Square 30.
x^{2}+60x+900=1422
Add 522 to 900.
\left(x+30\right)^{2}=1422
Factor x^{2}+60x+900. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+30\right)^{2}}=\sqrt{1422}
Take the square root of both sides of the equation.
x+30=3\sqrt{158} x+30=-3\sqrt{158}
Simplify.
x=3\sqrt{158}-30 x=-3\sqrt{158}-30
Subtract 30 from both sides of the equation.
Solution:
Nội dung chính Show
- For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768
- How do you find the smallest number by which a number must be multiplied to obtain a perfect cube?
- How do you find the smallest number by which 2560 must be multiplied so that the product is a perfect cube?
- What must be the least number multiply 217800 in orders to make it a perfect square?
- What is the smallest number by which 450 must be multiplied to get a perfect square?
We have to find the smallest whole number by which the number should be multiplied so as to get a perfect square number
To get a perfect square, each factor of the given number must be paired.
(i) 252
Hence, prime factor 7 does not have its pair. If 7 gets a pair, then the number becomes a perfect square. Therefore, 252 has to be multiplied by 7 to get a perfect square.
So, perfect square is 252 × 7 = 1764
1764 = 2 × 2 × 3 × 3 × 7 × 7
Thus, √1764 = 2 × 3 × 7 = 42
(ii) 180
Hence, prime factor 5 does not have its pair. If 5 gets a pair, then the number becomes a perfect square. Therefore, 180 has to be multiplied by 5 to get a perfect square.
So, perfect square is 180 × 5 = 900
900 = 2 × 2 × 3 × 3 × 5 × 5
Thus, √900 = 2 × 3 × 5 = 30
(iii) 1008
Hence, prime factor 7 does not have its pair. If 7 gets a pair, then the number becomes a perfect square. Therefore, 1008 has to be multiplied by 7 to get a perfect square.
So, perfect square is 1008 × 7 = 7056
7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
Thus, √7056 = 2 × 2 × 3 × 7 = 84
(iv) 2028
Hence, prime factor 3 does not have its pair. If 3 gets a pair, then the number becomes a perfect square. Therefore, 2028 has to be multiplied by 3 to get a perfect square.
So, perfect square is 2028 × 3 = 6084
6084 = 2 × 2 × 13 × 13 × 3 × 3
Thus, √6084 = 2 × 13 × 3 = 78
(v) 1458
Hence, prime factor 2 does not have its pair. If 2 gets a pair, then the number becomes a perfect square. Therefore, 1458 has to be multiplied by 2 to get a perfect square.
So, perfect square is 1458 × 2 = 2916
2916 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2
Thus, √2916 = 3 × 3 × 3 × 2 = 54
(vi) 768
Hence, prime factor 3 does not have its pair. If 3 gets a pair, then the number becomes a perfect square. Therefore, 768 has to be multiplied by 3 to get a perfect square.
So, perfect square is 768 × 3 = 2304
2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
Thus, √2304 = 2 × 2 × 2 × 2 × 3 = 48
☛ Check: NCERT Solutions for Class 8 Maths Chapter 6
Video Solution:
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768
NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3 Question 5
Summary:
For each of the following numbers, (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768 the smallest whole number by which it should be multiplied so as to get a perfect square number and the square root of the square number so obtained are as follows: (i) 7; √1764 = 42 (ii) 5; √900 = 30 (iii) 7; √7056 = 84 (iv) 3; √6084 = 78 (v) 2; √2916 = 54 and (vi) 3; √2304 = 48
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How do you find the smallest number by which a number must be multiplied to obtain a perfect cube?
Hence, the smallest number by which 100 must be multiplied to obtain a perfect cube is 2×5=10.
How do you find the smallest number by which 2560 must be multiplied so that the product is a perfect cube?
Hence, the smallest number by which it is multiplied = 25. Q. Q.
Expert-verified answer Therefore, we can conclude that, we must multiply both sides by 2 to make it a pair .
What is the smallest number by which 450 must be multiplied to get a perfect square?
Thus, we have to multiply by 450 by 2 to get a perfect square.
Therefore, we can conclude that, we must multiply both sides by 2 to make it a pair .
Expert-Verified Answer.
Given : Number 119019..
To find : least number should be added to 119019 to make it a perfect square.
Solution:.
6 is the least number to be added to 119019 to make it a perfect square.
Answer: Here, 2 does not forms a pair of square. So, 2 must be divided by 1152 to make it a perfect square.
To get a perfect square 2736 must be divided by 19.