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Because the number is the square of its units digit, it must be the square of a number between 1 and 9. Look at the squares of the first nine numbers.
The square of 1 is 1.
The square of 2 is 4.
The square of 3 is 9.
The square of 4 is 16.
The square of 5 is 25.
The square of 6 is 36.
The square of 7 is 49.
The square of 8 is 64.
The square of 9 is 81.
Of these numbers, 1, 25, and 36 are squares of their units digit.
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When the digits of a two digit number are reversed the new number is 36 more than the original number the units digit is twice the tens digit What is the original number?
17
What two digit number are interchanged to form a new two-digit number?
Any two digit number in which: (a) the units digit is not 0, and (b) the two digits are different will form a new 2-digit number when the digits are interchanged.
How do you find the surface area of a figure to the nearest square unit?
This is two problems. Surface area is measured in square units. The formulas for the area of different figures vary with the figures. The area of a regular four-sided figure is the length times the width. To round a number to a particular digit, look at the digit immediately to the right of your target, in this case, tenths of square units. If that digit is 4 or lower, zero it and everything to the right of it out. If that digit is 5 or higher, increase the target digit by one and zero everything to the right of it out. If your target digit is a 9, increasing it will turn it to zero and increase the digit to the left of it by one.
What is the units digit of the 5857th triangular number.?
The nth triangular number is given by ½ × n × (n+1)→ the 5857th triangular number is ½ × 5857 × 5858 = 17,155,153, so its units digit is a 3.------------------------------------------------------------Alternatively,If you look at the units digits of the first 20 triangular numbers they are {1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0}At this stage, as we are only concerned with the units digit, as we now have a 0 for the units digit, when 21 is added it is the same as adding 1 to 0 to give a 1, for the 22nd triangular number, we are adding 2 to the 1 to give 3, and so on - the sequence of 20 digits is repeating.To find the units digit of the nth triangular number, find the remainder of n divided by 20 and its units digit will be that digit in the sequence (if the remainder is 0, use the 20th number). To find the remainder when divided by 20 is very simple by looking at only the tens digit and the units digit:If the tens digit is even (ie one of {0, 2, 4, 6, 8}), the remainder is the units digitIf the tens digit is odd (ie one of {1, 3, 5, 7, 9}), the remainder is the units digit + 10.5857 ÷ 20 = ... remainder 17; the 17th digit of the above sequence is a 3, so the units digit of the 5857th triangular number is a 3.This trick can be used for much larger triangular numbers which calculators cannot calculate exactly using the above formula. eg the units digit of the 1234567890123456789th triangular number is... 1234567890123456789 ÷ 20 = .... remainder 9, so this triangular number's units digit is the 9th digit of the above sequence which is a 5.
What is the largest 3 digit square number?
961
