Square of a Number and Perfect Square Number

Find how many three-digit perfect cubes are there whose sum of the digits is a perfect square.

The units digit of square of a number and the units digit of cube of the number are equal to the units digit of the number. How many values are possible for the units digits of such numbers?

The least positive integer with which $3125$ should be multiplied so that the product is a perfect square is _____

The greatest $3$ digit number which is a perfect square is _____.

The smallest number with which $120$ should be multiplied, so that the product is a perfect square is _____.

Which of the following is not a perfect square?

What will be the units digit of the squares of the following numbers?

$71, 669, 2533 \& 30827$

$\left(\mathrm{i}\right) 1 \left(\mathrm{ii}\right) 9 \left(\mathrm{iii}\right) 8$

The smallest $4$ digit number which is a perfect square is _____. 

If $1+3+5+7+...$ up to $n$ odd numbers is equal to $n^2$, then find the value of $23+25+27+...+89$.

When a $\text{'}n\text{'}$ digit number is squared, then the number of digits in the square, thus, obtained is $2n-1,$ and _____.

The number of zeroes at the end of the square of a number is _____ the number of zeroes at the end of the number.

When a number is multiplied by itself, the product is said to be _____ of that number.

The length of a diagonal of a square plot is $24 cm$. Find the area of the square plot. The following steps are involved in solving the above problem. Arrange them in sequential order.

$\left(A\right)$ Area of the square plot$=\frac{1}{2}\times {\left(24\right)}^2=288 c{m}^2$

$\left(B\right)$ Given that the length of diagonal of a square plot $\left(d\right)=24 cm$

$\left(C\right)$ Area of a square, when diagonal is given is $\frac{1}{2}{d}^2$

Which of the following is not a perfect square?

Find the square of the following number using the identity $(a+b{)}^2=a^2+2ab+b^2$.

$635$

Find the square of the following number using the identity $(a+b{)}^2=a^2+2ab+b^2$.

$512$

Find the square of the following number using the identity $(a+b{)}^2=a^2+2ab+b^2$.

$208$

Giving reason, describe why the following number is not a perfect square.

$253,222$

Giving reason, describe why the following number is not a perfect square.

$134,387$

Giving reason, describe why the following number is not a perfect square.

$7923$