How that square of any positive integer Cannot be the form of 5q +2 or 5q 3 for any integer Q?

If r=4, then a=5m+4. is an integer. Hence, the square of any positive integer is not of form 5q+2 or 5q+3.

Which of the following Cannot be the square of any positive integer?

Hence, The square of any positive integer is of the form 5q, 5q + 1, 5q + 4 and cannot be of the form 5q + 2 or 5q + 3 for any integer q.

Is this possible to have the square of all positive integers?

It is not possible at all to have the squares of all the positive integers of the form 3m + 2. This can be explained by using Euclid’s Lemma,a= bq+r, 0≤ r

Is an odd integer then show that N square minus 1 is divisible by 8?

Answer Expert Verified P =2 then, 4P² + 4P = 4(2)² + 4(2) =16 + 8 = 24, it is also divisible by 8 . hence, we conclude that 4P² + 4P is divisible by 8 for all natural number . hence, n² -1 is divisible by 8 for all odd value of n .

Is it possible to have square of all positive integers of form 3m 2 where m is natural number?

where m is a integer. (3q + 2)2 = 9q2 + 12q + 4, which cannot be expressed in the form 3m + 2. Therefore, Square of any positive integer cannot be expressed in the form 3m + 2.

Are the square roots of all positive integers is rational if not give an example of the square root of a number that is rational number?

No, the square roots of all positive integers in not irrational. For example √9 = 3, √25 = 5, hence square roots of all positive integers is not irrational. For example, √25 = 5 is rational.

What would be the value of n for which and square minus 1 is divisible by 8?

Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p. ⇒ (n2 – 1) is divisible by 8. ⇒ n2– 1 is divisible by 8. Therefore, n2– 1 is divisible by 8 if n is an odd positive integer.

What will be n if’n square minus 1 is divisible by 8?

Hence, we can easily conclude that ${n}^2 – 1$ is divisible by 8 for any odd positive odd integer. Complete step by step answer: Any odd positive number is in the form of (4p + 1) or (4p + 3) for some integers p. Hence, ${n^2} – 1$ is divisible by 8 if n is an odd positive integer.

Can the square of any positive integer be of the form 3m 2 If yes give an example if not show why?

3 Answers. So, any positive integer is of the form 3k, 3k + 1 or 3k + 2. which is in the form of 3m and 3m + 1. Hence, square of any positive number cannot be of the form 3m + 2.

Can the number 4n N being a natural number end with the digit 0 justify your answer?

we know that any number ends with the digit 0 then whose factorisation is in the form of 2n*5n . but 4n doesnt contain the prime factor of 5 . hence 4n never ends with 0.

Are the square root of all positive?

Statement (A): No, the square roots of all positive integers are not irrational. Because we know that the square roots of all positive integers includes both rational and irrational numbers.

Are the square roots of all non negative integers irrational Support your answer with suitable examples?

No the square roots of all non negative integers are not irrational. The square root of all non negative integers that are perfect squares, are rational. For eg. For example √2, √5, √7 are irrational numbers.

Is the square of any positive integer 5q + 2 or 5q+3?

Let a be any positive integer. ∴ a = 5m when r = 0, a = 5m + 1 when r = 1, a = 5m + 2 when r = 2, a = 5m + 3 when r = 3, a = 5m + 4 when r = 4 From all these cases, it is clear that square of any positive integer cannot be of the form 5q + 2 or 5q + 3.

Can the square of any positive integer be in the form 5m+2?

Show that square of any positive integer cannot be in the form 5m+2 or 5m+3 for some integer m. See what the community says and unlock a badge. Refer to the attatchment.

What is the value of 5Q+2 in least significant digit?

5q+2 must end in 2 (if q is off) or 7 (if q is even) as the Least Significant Digit. 5q+3 must end in 3 or 8. Any integer p must have its LSD = the LSD of the square of its LSD. (e.g. the LSD of the square of 8327 is the same as the LSD of the square of 7 i.e. 9 in this example.)

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