Are there numbers whose squares are smaller than the number themselves rewrite it

Mathematics

1 answer:

Elan Coil [88]3 years ago

4 0

Numbers greater than zero but less than one have squares that are smaller.

Consider the number one-half (1/2); half of a half is a quarter (1/4 < 1/2)!

Of course, the square of a negative number is greater (since a negative squared is positive).

Only the numbers zero and one are equal to their squares.

another explanation:

Yes .

In fact there is an infinite number of numbers that have that condition. For example (1/2)² = 1/4.

In fact any positive number ’n’ such that 0<n<1 is a number which has a smaller number when squared.

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The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the

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6 if 7 doesnt divide n, 42 otherwise. The only possible options are those 2.

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$16 = 2^4$ , thus, 16 only has 2 as a prime divisor. We conclude that n = 4*k, with k an odd number. On the other hand, $45 = 3^2 * 5$ , since the greatest factor between n and 45 is 3, then 5 is not a divisor of n, and n has the form 3*j, with j not a multiple of 3. Since 3 and 4 doesnt have common primes as factors, then j = 4*l, with l odd.

Thus n = 12 * j, with j a number that satisfies:

3 is not a divisor of j
2 is not a divisor of j
5 is not a divisor of j

Note that $210 = 2*3*5*7$ . 12 is not factor of 210, but 6 is. j doesnt have any prime divisor in common with 210, with the exception, maybe, of 7. So the greatest common factor of them is 1 or 7, depending on weather 7 divides j (or equivalently, n) or not. Therefore, the greatest common factor of n and 210 could be 6, if 7 does not divide n, or 6*7 = 42, if 7 divides n.