Properties of Square Numbers

Find the positive square root of the following by the factorization method:

$28\frac{189 }{289 }$

Find the positive square root of the following by the factorization method:

$38\frac{139 }{169 }$

Find the largest five digit perfect square.

Find the least number which when subtracted from $18265$ makes the remainder a perfect square.

Find the value of the following. ${56}^{2 }$

In a school Ramu friends divided into four groups. Each of the group takes the number of buttons and make different kinds of squares with them. The second group took $12$ buttons.

There are _____ buttons in each column.

In a school Ramu friends divided into four groups. Each of the group takes the number of buttons and make different kinds of squares with them. The second group took $12$ buttons.

There are _____ buttons in each row.

The students of class three have been made to stand in a square. There are $13$ students in the first row. After some time, a few students went away. The remaining students could still be arranged in a square with $10$ students in a row. How many students went away?

Place the correct number in the empty spaces.

$$\begin{gathered} 3^2=3\times 3=\_\_\_\_\_ \\ {4}^2=\_\_\_\_\_ \times \_\_\_\_\_ =\_\_\_\_\_ \\ \_\_\_\_\_ = \_\_\_\_\_ \times \_\_\_\_\_ =25 \\ \_\_\_\_\_ = \_\_\_\_\_ \times \_\_\_\_\_ =36 \end{gathered}$$

What is the value of ${101}^2-{100}^2$?

What will be the number of zeros in the square of $400$?

Write five numbers which you can decide by looking at their units digit that they are not square numbers.

Using properties of squares, find the values of the following.

${150}^2-{149}^2$

Using properties of squares, find the values of the following.

${121}^2-{120}^2$

Using properties of squares, find the values of the following.

${100}^2-{99}^2$

Using properties of squares, find the values of the following.

${45}^2-{44}^2$

Which of the following is a perfect square?

$38, 96, 21, 245, 900$

Find the greatest number of two digits which is a perfect square.

Evaluate :

${\left(2000\right)}^2-(1999{)}^2$

Evaluate :

${\left(1001\right)}^2-(1000{)}^2$