# What are we learning ?

**Competency in Focus:**Perfect square numbers This problem from American Mathematics contest (AMC 10A, 2014) is based on the concept that when a number is a perfect square .

# First look at the knowledge graph.

# Next understand the problem

Which of the following numbers is a perfect square?

##### Source of the problem

American Mathematical Contest 2014, AMC 10A Problem 8

##### Key Competency

This number theory problem is based on the concept that when a number is a perfect square

##### Difficulty Level

5/10

##### Suggested Book

Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

# Start with hints

Do you really need a hint? Try it first!

First of all look at the examples , see that for all positive , we have.Now what we have to do with this ?

Now we have to find which member has what uniform numbers from the given conversation .

After some simple manipulations , we have . Thus now the problem reduces to finding a value of such that is a perfect square.

Since is a perfect square, we must also have be a perfect square. In order for to be a perfect square, must be twice a perfect square.

Now check the options and see for what value of n , must be twice a perfect square. works, thus, and our desired answer is

# Connected Program at Cheenta

#### Amc 8 Master class

Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.

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