Question

express the following as the the sum of two consecutive natural numbers 27 square​

Answer 1

☆Answer☆

$\sf {{27}^{2} }$= 364 + 365

Step-by-step explanation-

We have to use given formula-

$\huge\rm\red {{n}^{2} = \frac{ {n}^{2} - 1}{2} + \frac{ {n}^{2} + 1 }{2}}$

• ${{n}^{2}}$ = given natural number ( 27^2)

Now, putting values

$\huge\sf\blue { {27}^{2} = \frac{ {27}^{2} - 1}{2} + \frac{ {27}^{2} + 1 }{2}}$

$\sf {=>{27}^{2} = \frac{729 - 1}{2} + \frac{729 + 1}{2}}$

$\sf {=> {27}^{2} = \frac{728}{2} + \frac{730}{2}}$

$\sf\green { =>{27}^{2} = 364 + 365 \: ans..}$

__...

Hence, $\sf {{27}^{2} }$ is the sum of two consecutive natural numbers which are 364 and 365.

Answer 2

Answer:

Required expression is ${27}^{2} = 365 + 364$

Step-by-step explanation:

We can write,

${n}^{2} = \frac{ {n}^{2} + 1}{2} + \frac{ {n}^{2} - 1 }{2}$

We are putting n = 27,

${27}^{2} = \frac{ {27}^{2} + 1 }{2} + \frac{ {27}^{2} - 1 }{2} \\ = \frac{729 + 1}{2} + \frac{729 - 1}{2} \\ = \frac{730}{2} + \frac{728}{2} \\ = 365 + 364$

Therefore, required expression is ${27}^{2} = 365 + 364$ where 364 and 365 are consecutive numbers.

This is a problem of Mathematics.

Some important Mathematics formulas:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Two more important Mathematics problem:

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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