Question

the sum of certain consecutive odd numbers starting from 9 to 3120.what is the perfect square succeeding 3120?
a) 3145
b)3136
c)3138
d)3142

Answer 1

3136 is the perfect square succeeded 3120

Answer 2

Answer:

Option B is the right answer.

3136 is the perfect square succeeding 3120.

Step-by-step explanation:

In this question, we have to find out the perfect square succeeding $3120$.

Before beginning with the solution let us try and understand the concept of perfect squares.

A perfect square is simply an integer or a number that can be written as the square of another number. It is basically the product of the same integer multiplied by itself.

Some examples of perfect squares are:

$25 = 5\times 5$

$49 = 7 \times 7\\9 = 3 \times 2\\4 = 2 \times 2$

Let us now check for a perfect square in each given option by finding their L.C.M.

$3145$= The prime factors are $5, 17, \ and\ 37$. Hence, it is not a perfect square.

$3136$= $56 \times 56$. Hence, it is a perfect square.

$3138$= Any number that ends with $2, 3, 7, \ or \ 8$ can never be perfect squares. Hence, $3138$ is not a perfect square.

$3142$= Any number that ends with $2, 3, 7, \ or \ 8$ can never be perfect squares. Hence, $3142$is not a perfect square.

Final Answer:

Hence, 3136 is the perfect square succeeding 3120.

Option B is the right answer.

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