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The prime factorization of 420 is 2 x 2 x 3 x 5 x 7. You need another 3 x 5 x 7 (105) to make that a perfect square. The question should stipulate integral values. If k was 1/105 or 1/420, the value would also be a perfect square.

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7y ago
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7y ago

The answer is k = 105.

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Q: What Is The Smallest Value Of k For 420k To Be A Perfect Square?
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Rolls Royce Motor Cars are manufactured via a "bespoke" process on a mechanized and computerized assembly line, but most of this process of putting the components together are done by hand. A RR engine is put together usually by one person and by hand. It takes approximately three and a half months from order and deposit to delivery depending on production priorities. Order a limited production run, or one of the coupes, or any special edition that will be rare (ie "Centenary Edition" or "Phantom Black"), or a car that has been "tricked out" with lots of bespoke options (not on the options list but put in the car anyway, like an exclusive color or an extra refrigerator, or wood veneer in places it normally isn't)--such cars take longer to delivery time, usually around 6 months, sometimes up to a year. The rarer the car the longer the time. 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If you opt to standard ship it overseas by boat (takes about 7-10 days to North America), the regional Rolls Royce Office in the country the dealer is located (ie Rolls Royce North America Port Elizabeth, NJ) will keep it for another week to make sure Goodwood stamped all the bugs out. This is the problem with bespoke cars. Yes, it's nice to open the door, look at the colors, fabrics, materials, and features to know this is YOUR car, but because they are put together by hand, this allows for more quality control errors--humans are not perfect. The car must be tested over and over to ensure it will be as little as problematic as possible (notice how I word this). Another reason why the warranty starts at delivery and not at mileage 0. Your new Phantom may be delivered with a couple of dozen miles on it. 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That's the quandary of these vehicles-you have to consider when is a problem is really a problem. You will never see a brand new Rolls Royce car delivered with 0 or less than 10 miles. I don't care if Ian Robertson (RR CEO) himself logs on and differs; that means somebody over there at the plant wasn't doing their job, and I don't think RR would even allow such a thing. This is what the bespoke process is all about--it is about craftsmanship and excellence, to pamper you and your car while making it and getting the bug out. . It is then the salesman's responsibility to ship your car from regional to the dealer. If the dealer is close to the regional your salesman may actually drive your car him/herself to the dealer where you purchased the car. No car carrier tractor trailer, and most cases you don't want one--these cars were not meant to be towed or hauled as inventory, your Ford Taurus was. This is when your car is prepped for delivery (wash, wax, mats, plates, registration, etc.) For an extra charge you can have your new Phantom from the factory put on a 747 jumbo cargo jet to be shipped anywhere you want in the world for your salesman to be there to hand you the key. . . Roll Royce usually delivers their products to the new owner's residence or work place with an on-site orientation on the car's features, and to my knowledge, rarely does a customer come into the dealer to take delivery, like most of us do when we buy a new car. I've seen a Mercedes S-Class delivered that way but not sure for that brand if that's the norm. Open the hood and look at the pretty V12 engine, BUT DON'T TOUCH IT. EVER. You might invalidate the warranty--if you need so much as a replacement light bulb, for 4 years or 48,000 miles from the key hand-over, one will be provided FREE--as well as all the other servicing and maintenance requirements. 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