Answer: Option A. -> True
:
A
${18}^2+{24}^2=324+576=900={30}^2$
Since the squares of 18 and 24 add up to the square of 30, the numbers 18, 24 and 30form a Pythagorean triplet, and hence, can be used to represent the three sides of a right- angled triangle.

Answer: Option A. -> 32, 45
:
A
$1024=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
$=2^2\times 2^2\times 2^2\times 2^2\times 2^2\Rightarrow \sqrt{\left(1024\right)}=\sqrt{(2^2\times 2^2\times 2^2\times 2^2\times 2^2)}=2\times 2\times 2\times 2\times 2=32$
$2025=3\times 3\times 3\times 3\times 5\times 5$
$=3^2\times 3^2\times 5^2\Rightarrow \sqrt{\left(2025\right)}=\sqrt{(3^2\times 3^2\times 5^2)}=3\times 3\times 5=45$

Answer: Option A. -> 58
:
A
$\text{Given number: 3364}$
$\text{By grouping the numbers from the}\text{left, we get}\overline{33}\overline{64}.$
$\text{Now, perform the long division.}$
$\begin{array}{cc}& 58\\ 5& \overline{33}\overline{64}\\ & 25\downarrow \\ 108& 864\\ & 864\\ & 0\end{array}$
$\text{Thus, the square root of 3364 is 58.}$

Answer: Option B. -> 63
:
B
Number of trees = 1024. Since number of rows = number of columns, this means that the number of trees is a perfect square. Therefore number of rows/columns = square root of 1024 (number of trees).
$\sqrt{1024}$= $\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}=32$
Therefore, the initial number of rows/columns = 32. After cutting 1 row and one column, number of rows/columns = 32-1 = 31.
The remaining number of trees = ${31}^2$.
Therefore, number of trees that were cut = ${32}^2-{31}^2$ = 1024 - 961 = 63.

Answer: Option D. -> 150
:
D
Between the squares of any two consecutive numbers n and (n+1), lie 2n non-perfect squares.
Therefore between squares of 75 and 76 (n = 75 and n + 1 = 76), lie (2 x 75) = 150 non-perfect squares.

Answer: Option C. -> 30
:
C
Since the square sheet needs to be divided equally into 4, 5, and 6 equal parts respectively, its area must be a perfect square divisible by 4, 5, and 6; or the area of the square sheet should be a multiple of 4, 5, and 6.
L. C. M. of 4, 5, and 6 = 60. But 60 is not a perfect square.
$60=2\times 2\times 3\times 5=2^2\times 3\times 5$.
If we multiply the LCM by 3 and 5 both, it will become a perfect square. Therefore the minimum area of the square sheet $=60\times 3\times 5=900$ sq. units.
Now 900 is a minimum perfect square, which is divisible by 4, 5, and 6. Therefore the side of the square should be the square root of the area of the square (Area of a square = $sid{e}^2$ sq. units).
Hence, the minimum length of the side of the square = $\sqrt{\left(900\right)}=\sqrt{(2^2\times 3^2\times 5^2)}$ = 30 units.

Answer: Option B. -> 200
:
B
$\sqrt{2}=1.4142$ (Given)
Multiply both sides by $10$
$10\times \sqrt{2}=14.142$
$\sqrt{100\times 2}=14.142$
Squaringboth sides, we get thesquare of $14.142$ to be approximately equal to $200$.

Answer: Option A. -> perfect square
:
A
If m can be expressed as $n^2$, where n is a natural number then, m is called a perfect square.

Answer: Option C. -> 1521
:
C
$\text{The number 39 ends with 9.}\text{And}{9}^2=81\text{which ends with 1.}\text{Hence,}{39}^2\text{should have 1 in the units}\text{place.}$
$\text{We can observefrom options that}\text{only 1521 satisfies this.}\text{Hence 1521 is the answer.}$
$\text{Alternatively, 39 should be multiplied}\text{with 39 to obtain the square.}$
$\text{So,}39\times 39=1521.$

Answer: Option B. -> Perfect squares
:
B
When an integer is multiplied by itself, it results in a perfect square.
When we square integers like 1, 2, 3, 4, 5, ...,we obtain 1, 4, 9, 16, 25, ... .
Hence, the given numbers which are obtained by squaring the integers are known as perfect squares.