Example 11 Find The Greatest 4 Digit Number Which Is A Perfect Transcript. example 11 find the greatest 4 digit number which is a perfect square. greatest 4 digit number = finding square root of 9999 by long division here, remainder = 198 since remainder is not 0, so, 9999 is not a perfect square we need to find the greatest 4 digit number which is a perfect square so, we need to find a number smaller than 9999, as numbers bigger than 9999 are 5 digit. The remainder is 198. this shows 992 is less than 9999 by 198. this means, if we subtract the remainder from the number we get a perfect square. therefore the required perfects square is 9999−198 = 9801. and √9801 = 99.
Example 11 Find The Greatest 4 Digit Number Which Is A Perfect The greatest perfect square of a 4 digit number . an integer that can be expressed as the square of another integer is called a perfect square. square of 100 is 10000 which is the first 5 digit number, so the required number must be less than 10000 which means the square root must be less than 100. so, the next number must be 99, and the square. The digital root of our number is not equal to 0, 1, 4, or 7. our number cannot be a perfect square. 2nd example: 21904. does the number ends with 1, 4, 5, 6, 9, or 00? yes, our number might be a perfect square. our number ends with 4 — is its ten's digit an even number? yes, its ten's digit is 0. our number might be a perfect square. what's. Problem 1: find the perfect squares between 30 and 40. solution: we see that between 30 and 40 we get a number 36 whose only square root is 6 i.e., if we multiply 6 by itself then we get 36. thus 36 is the only number that is a perfect square between 30 and 40. problem 2: find the greatest 4 digit number which is a perfect square. Sum. solution. greatest number of 4 digits = 9999. we find 9999 by long division method. the remainder is 198. this shows 99 2 is less than 9999 by 198. this means if we subtract the remainder from the number, we get a perfect square. therefore, the required perfect square is 9999 198 = 9801. and, 9801 = 99.
Example 11 Find The Greatest 4 Digit Number Which Is A Perfect Problem 1: find the perfect squares between 30 and 40. solution: we see that between 30 and 40 we get a number 36 whose only square root is 6 i.e., if we multiply 6 by itself then we get 36. thus 36 is the only number that is a perfect square between 30 and 40. problem 2: find the greatest 4 digit number which is a perfect square. Sum. solution. greatest number of 4 digits = 9999. we find 9999 by long division method. the remainder is 198. this shows 99 2 is less than 9999 by 198. this means if we subtract the remainder from the number, we get a perfect square. therefore, the required perfect square is 9999 198 = 9801. and, 9801 = 99. For example, to check whether 21 is a perfect square or not, let us calculate its square root. √21 = 4.58. as we can see, 4.58 is not a whole number integer, so, 21 is not a perfect square number. let us take another example of the number 64 → √64 = 8. we can see that 8 is a whole number, therefore, 64 is a perfect square. Hence it is a perfect square and it is clear that our number will be one less than 100. so, our desired answer is 992 = 9801 99 2 = 9801, hence, our desired 4 – digit number with a perfect square is 9801 and its square root is 99. note: one might get confused that how do we know 4 – digit largest number and for the smallest 5 – digit we.
Comments are closed.