All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CAT Exam  >  CAT Questions  >  What is the least no by which 2800 should be ... Start Learning for Free
What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none?
Clear all your CAT doubts with EduRev
Most Upvoted Answer
What is the least no by which 2800 should be multiplied so that the pr...
Solution:
To make 2800 a perfect square, we need to multiply it with a number such that the product is a perfect square. Let that number be x.
Prime factorization of 2800 = $2^3$ × $5^2$ × $7$
For the product to be a perfect square, each prime factor must have an even power.
Let the power of 2 be a, power of 5 be b, and power of 7 be c.
Therefore, x should be such that:
$2^a$ × $5^b$ × $7^c$ is a perfect square
Applying the condition for a perfect square, a, b, and c should be even.
The least value of x to make 2800 a perfect square is obtained by taking the smallest even powers of 2, 5, and 7.
Hence, the least value of x is 2 × 5 × 7 = 70.
Therefore, option (2) is correct.
HTML Code:
Solution:

To make 2800 a perfect square, we need to multiply it with a number such that the product is a perfect square. Let that number be x.

Prime factorization of 2800 = $2^3$ × $5^2$ × $7$

For the product to be a perfect square, each prime factor must have an even power.

Let the power of 2 be a, power of 5 be b, and power of 7 be c.

Therefore, x should be such that:

$2^a$ × $5^b$ × $7^c$ is a perfect square

Applying the condition for a perfect square, a, b, and c should be even.

The least value of x to make 2800 a perfect square is obtained by taking the smallest even powers of 2, 5, and 7.

Hence, the least value of x is 2 × 5 × 7 = 70.

Therefore, option (2) is correct.
Community Answer
What is the least no by which 2800 should be multiplied so that the pr...
Let us take 7 and multiply it with 2800 we get 19600 which is a perfect square of 140
140*140= 19600..
So the correct option is 7
Thank you.
Explore Courses for CAT exam

Similar CAT Doubts

Directions: Read the following information carefully and answer the given question.A minimum viable product (MVP) is a development technique in which a new product or website is developed with sufficient features to satisfy early adopters. The final, complete set of features is only designed and developed after considering feedback from the product's initial users. This technique helps them in making the final product much better. With the help of MVP concept, the research or the marketing team will come to know where the product is lacking and or what are its strengths or weaknesses.MVP has three distinct features. One is that it will have enough features for consumers to purchase the product (it becomes easier for the company to market it), the other is that it will have some sort of a feedback mechanism wherein users would be able to send their feedback about the product. And, lastly it should have enough future benefits for consumers who choose to adopt the product first (Google gave free upgrade of its OS to all Nexus users). The idea is to get feedback from the consumers which will in turn help in making the desired changes in the final product. MVP actually tests the usage scenario that is much more helpful for the company to make changes to the final product.The developing team of an MVP will not waste any time on anything beyond the bare minimum, and build every other feature over time as they assess the customers' wishes and preferences as they start using the product. The product may change even dramatically or even get abandoned as feedback from users may significantly diverge from the original project. However, the developing teams will not waste any resources (efforts, time, money, advertising) on a product that no one really wants, needs, or likes. The catch to this development technique is that it assumes that early adopters can see the vision or promise of the final product and provide the valuable feedback needed to guide developers forward.The whole focus is learning during product development by collecting information from customers that are validated already. Observing users as they utilize the product is much more reliable than trying to validate marketing hypotheses with questionnaires or forecasts. A common pitfall is to release a bare-bone product that is so much below the users' expectations that is not viable at all. In general, the MVP technique is particularly viable for technically-oriented products used by technical users who are often keen on providing practical insights on how to improve or update the product. The concept of MVP has, in fact, been widely adopted by many verticals in the informatics industry. For example, many video games today spend many months (sometimes years) as early access products and are slowly developed as the community grows. Some popular franchises, such as Farmville, fully leveraged the concept of MVP by implementing new gameplay features over time while progressively improving overall user experience.Q. Which of the following statements is true in context of the passage?

A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals – FDA or EU.The following facts are also known: There were equal numbers of domestic and foreign products. Half of the domestic products were FDA approved cosmetic products. None of the foreign products had both the approvals, while 60 domestic products had both the approvals. There were 140 nutrition products, half of them were foreign products. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.Q.Which among the following options best represents the number of domestic cosmetic products that had both the approvals?

Top Courses for CATView all

Top Courses for CAT

What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none?
Question Description
What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none?.
Solutions for What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? defined & explained in the simplest way possible. Besides giving the explanation of What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none?, a detailed solution for What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? has been provided alongside types of What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? theory, EduRev gives you an ample number of questions to practice What is the least no by which 2800 should be multiplied so that the product may be a perfect square 1)2. 2)7 3)14. 4)none? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup