Question

Express 13 square as the sum of two consecutive natural numbers

Answer 1

Step-by-step explanation:

square of 13 is 169

n+(n+1)=169

2n=169-1

n=168÷2

n=84

n+1=85

Answer 2

The two consecutive natural numbers whose sum is equal to 13² are 84 and 85.

Given,

The number = 13².

To find,

Express this as the sum of two consecutive natural numbers.

Solution,

We can see that here, the given number is 13².

Now, to represent the given number as the sum of two consecutive natural numbers, first, let's assume the two consecutive natural numbers be

$n,n+1.$

The sum of these numbers will be

= n + (n + 1)

Also, as we know that the square of 13 is,

13² = 169.

According to the given condition,

n + (n + 1) = 169

Simplifying,

2n + 1 = 169

⇒ 2n = 169 - 1

⇒ 2n = 168

$\implies n = \frac{168}{2} = 84$

⇒ n = 84.

So,

one of the numbers = n = 84, and,

the other number = n + 1 = 84 + 1 = 85.

⇒ the two consecutive numbers = 84, 85.

Therefore, the two consecutive natural numbers whose sum is equal to 13² are 84 and 85.

#SPJ3