Random Interesting Patterns Followed by Square Numbers

Q.

Find the square root of $7056$ by prime factorization method

Q.

The next number in the sequence $4,9,25,49.....$ will be?

Q.

Question 5
Observe the following pattern and supply the missing numbers.

${11}^2=121{101}^2=10201{10101}^2=102030201{1010101}^2=.........................{.}^2=10203040504030201$

Q.

Find the square root of $31$ in the simplest form?

Q.

Question 4
Observe the following pattern and find the missing digits.

${11}^2=121{101}^2=10201{1001}^2=1002001{100001}^2=\mathrm{1....2....1}{10000002}^2=\mathrm{1...........}$

Q.

Find the square root of $1764$ by prime factorization method

Q.

Write the smallest $5-$digit number in figures and words

Q.

Using the pattern 11² = 121 and 111² = 12321, we get 1111² =

1. 12321

2. 1234321

3. 1423241

4. 123454321

Q. Last year my age was a square number. Next year my age will be cube number. What is my age ?

Q. Which whole number is closest to the square root of 350?

Q.

If a number has 1 or 9 in the unit's place, then it's square ends in

1. 9

2. 1

3. 3

4. 8

Q.

Square of the $431$ is even or odd:

Q.

Find the square root of $784$.

Q.

Question 96

Solve the following question:

Using prime factorization, find the square roots of

a) 11025
b) 4761

Q. How to find Squares and Square Roots ?

Q.

Question 3 (i)
The squares of which of the following would be odd number:

431

Q.

The value of

$(111111{)}^2$

1. $12345654321$
2. $12345432169$
3. $13243563429$
4. $12376589431$

Q. A teacher wants to arrange 2, 800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

Q.

Question 132

Solve the following question:

The area of a square plot is $101\frac{1}{400}{m}^2$. Find the length of one side of the plot.

Q. Prove that the square of any positive integer is of form $5q,5q+1,5q+4$ for some integer $q$.

Q.

Square of the $2826$ is even or odd:

Q.

Area of square park whose perimeter is $320m.$

Q.

$\text{Find the value of}(66666{)}^2.$

1. 222237776

2. 445544554455

3. 4444355556

4. 4444655556

Q.

How to solve the square root of $576$?

Q. (i) Find the value of $(666{)}^2$
(ii) Find the value of $(66666{)}^2$

Q. The squares of which of the following would be odd numbers:
$431$
$2826$
$7779$
$82004$

1. $431$ and $7779$
2. $431$ and $2826$
3. $2826$ and $7779$
4. $2826$ and $82004$

Q.

Question 3 (ii)
The squares of which of the following would be odd number:

2826

Q. If $(x-\frac{1}{x})=6,$ find the value of $(x^2+\frac{1}{x^2})$ and $(x^4+\frac{1}{x^4})$

Q. How to get cube root through estimation ?

Q.

Question 3 (i)
The squares of which of the following would be odd number:

431