| Hint: Here make use of the concept that for a number to be a perfect square it should end with either $1,4,5,6,9,00$ (even number of 0’s). Complete step-by-step answer: Show $23453$ $7928$ $222222$ $64000$ The number $89722$ ends with 2 and does not with $1,4,5,6,9,00$ or even number of 0’s at the end. $222000$ $505050$ Note: The number to be a perfect square should satisfy the first condition that it should end with either $1,4,5,6,9,00$ or even a number of zeroes. (i) 1296 We know that  It can be written as 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 Here After pairing the same prime factors, no factor is left. Therefore, 1296 is a perfect square of 2 × 2 × 3 × 3 = 36. (ii) 1764 We know that It can be written as 1764 = 2 × 2 × 3 × 3 × 7 × 7 Here After pairing the same factors, no factor is left. Therefore, 1764 is a perfect square of 2 × 3 × 7 = 42. (iii) 3025 We know that It can be written as 3025 = 5 × 5 × 11 × 11 Here After pairing the same prime factors, no factor is left. Therefore, 3025 is a perfect square of 5 × 11 = 55. (iv) 3969 We know that It can be written as 3969 = 3 × 3 × 3 × 3 × 7 × 7 Here After pairing the same prime factors, no factor is left. Therefore, 3969 is a perfect square of 3 × 3 × 7 = 63. (i) 729 We know that It can be written as 729 = 3 × 3 × 3 × 3 × 3 × 3 Here 729 is the product of pairs of equal prime factors Therefore, 729 is a perfect square. (ii) 5488 We know that It can be written as 5488 = 2 × 2 × 2 × 2 × 7 × 7 × 7 Here After pairing the same prime factors, one factor 7 is left unpaired. Therefore, 5488 is not a perfect square. (iii) 1024 We know that It can be written as 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Here After pairing the same prime factors, there is no factor left. Therefore, 1024 is a perfect square. (iv) 243 We know that It can be written as 243 = 3 × 3 × 3 × 3 × 3 Here After pairing the same prime factors, factor 3 is left unpaired. Therefore, 243 is not a perfect square. Formally, a string is a finite, ordered sequence of characters such as letters, digits or spaces. The empty string is the special case where the sequence has length zero, so there are no symbols in the string. There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments, the empty string is denoted with ε or sometimes Λ or λ. The empty string should not be confused with the empty language ∅, which is a formal language (i.e. a set of strings) that contains no strings, not even the empty string. The empty string has several properties: In context-free grammars, a production rule that allows a symbol to produce the empty string is known as an ε-production, and the symbol is said to be "nullable". Use in programming languages[edit]In most programming languages, strings are a data type. Strings are typically stored at distinct memory addresses (locations). Thus, the same string (for example, the empty string) may be stored in two or more places in memory. In this way, there could be multiple empty strings in memory, in contrast with the formal theory definition, for which there is only one possible empty string. However, a string comparison function would indicate that all of these empty strings are equal to each other. Even a string of length zero can require memory to store it, depending on the format being used. In most programming languages, the empty string is distinct from a null reference (or null pointer) because a null reference points to no string at all, not even the empty string. The empty string is a legitimate string, upon which most string operations should work. Some languages treat some or all of the following in similar ways: empty strings, null references, the integer 0, the floating point number 0, the Boolean value false, the ASCII character NUL, or other such values. The empty string is usually represented similarly to other strings. In implementations with string terminating character (null-terminated strings or plain text lines), the empty string is indicated by the immediate use of this terminating character. Examples of empty strings[edit]The empty string is a syntactically valid representation of zero in positional notation (in any base), which does not contain leading zeros. Since the empty string does not have a standard visual representation outside of formal language theory, the number zero is traditionally represented by a single decimal digit 0 instead. Zero-filled memory area, interpreted as a null-terminated string, is an empty string. Empty lines of text show the empty string. This can occur from two consecutive EOLs, as often occur in text files, and this is sometimes used in text processing to separate paragraphs, e.g. in MediaWiki. Is 5488 a perfect square give reason in support of your answer?After pairing the same prime factors, one factor 7 is left unpaired. Therefore, 5488 is not a perfect square. After pairing the same prime factors, there is no factor left. Therefore, 1024 is a perfect square.
IS 408 a perfect square give reason?Since the number 408 has 8 at its unit's place, it is NOT a perfect square.
Are the following numbers perfect square give reason?Solution: The square of a number having 0, 1, 4, 5, 6 or 9 at its unit place is perfect squares. Also, the square of a number can only have an even number of zeros at the end. (vi) 89722 (vii) 222000 (viii) 505050 are 7, 3, 8, 2, 000, 2, 000, 0 respectively.
What is a perfect square numbers Class 8?Perfect Square Numbers
We know that the square of a number is that number times itself. In other words, the perfect squares are the squares of the whole numbers such as 1 or 12, 4 or 22, 9 or 32, 16 or 42, 25 or 52 and so on.
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