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15 is a triangular number.

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Important Questions on Squares and Square Roots

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In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

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Which number will replace the question mark?

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In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

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HARD
Let E denote the set of all natural numbers n such that 3<n<100 and the set {1,2,3,,n} can be partitioned into 3 subsets with equal sums. Find the number of elements of E.
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A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
HARD
Let a and b be natural numbers such that 2a-b, a-2b and a+b are all distinct squares. What is the smallest possible value of b ?
EASY

Select the combination of letters that when sequentially placed in the blanks of the given series will complete the series.

l _ chtlgc _ tlg _ ht _ gc _ tlgch _

EASY
The smallest integer with 4 digits which is a perfect square is:
EASY

If, in a two-digit number, the digit at unit place is x and the digit at tens place is 4, then the two-digit number is _____.

EASY
If in a certain way, 3  +  4  =  25 and 7  +  24  =  625, then 9  +  40  =  ?
EASY
What is the least number that should be added to the product of 7×8×9×10 to make it a perfect square?
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Consider the set A of natural numbers n whose units digit is non-zero, such that if this units digit is erased, then the resulting number divides n. If K is the number of elements in the set A, then
EASY
Prove that the product of 2 consecutive even numbers added to 1 gives a perfect square.
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In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

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The unit digit in the expression 55725+735810+22853 is 
EASY
Which is the smallest perfect square number exactly divisible by 4, 5, 6 and 9 ?
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Which number will replace the question mark?

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HARD
The number of all 2-digit numbers n such that n is equal to the sum of the square of digit in its tens place and the cube of the digit in units place is
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Consider a three-digit number with the following properties:

I. If its digits in units place and tens place are interchanged, the number increases by 36
II. If its digits in units place and hundreds place are interchanged, the number decreases by 198 .

Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number

EASY
Find the value of the letters in the following

A1+1BB0