Question

Find the square root of 12.25 using a long division method.
A. 3.2
B. 3.4
C. 3.5
D. 3.1

Answer 1

HINT:-A square root of a number is a value that, when multiplied by itself, gives the number. For example:\[~4\times 4\] = 16. Therefore, 4 is the square root of 16. Using this we can solve the above problem.

Complete step by step answer:
PERFECT SQUARE: A square number or a perfect square is an integer that is obtained by multiplying an integer by itself. For example, 9 is a square number or we can say that 9 is a perfect square because \[3\times 3\] is 9.
We will solve this question using the long division method.
\[3\overset{3.5}{\overline{\left){\begin{align}
  & 12.25 \\
 & \dfrac{-9}{65\overline{\left){\begin{align}
  & 325 \\
 & \dfrac{-325}{00} \\
\end{align}}\right.}} \\
\end{align}}\right.}}\]
So, as we can observe that the quotient of this division is 3.5.
Therefore, the square root of 12.25 is 3.5.
Hence, the answer of this question is (c).
NOTE:-
Let us now know the properties of Perfect Square numbers.
1. The numbers that are perfect squares end with 1, 4, 5, 6 and 9.
2. The numbers that end with 2, 3, 7 and 8 are not perfect squares.
3. The square of a natural number other than one is either a multiple of 3 or exceeds a multiple of 3 by 1.
4. The square of a natural number other than one is either a multiple of 4 or exceeds a multiple of 4 by 1.
5. The number of zeros at the end of a perfect square is always even.