Question

Write down the square roots of
1) 25
2) 49
3) 81
4) 169
5) 225
6) 324
7) 64
8) 121
9) 361

Answer 1

Hint:
First, we will find the square root a number is a value that when multiplied by itself given the number. Then we will use the given definition in the given options to find the required value.

Complete step by step solution:
We know that the square root of a number is a value that, when multiplied by itself given the number.

1) We are given that the number is 25.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {25} = \sqrt {5 \times 5} \\
   \Rightarrow \sqrt {25} = 5 \\
 \]

Thus, the square root of 25 is 5.

2) We are given that the number is 49.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {49} = \sqrt {7 \times 7} \\
   \Rightarrow \sqrt {49} = 7 \\
 \]

Thus, the square root of 49 is 7.

3) We are given that the number is 81.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {81} = \sqrt {9 \times 9} \\
   \Rightarrow \sqrt {81} = 9 \\
 \]
Thus, the square root of 81 is 9.

4) We are given that the number is 169.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {169} = \sqrt {13 \times 13} \\
   \Rightarrow \sqrt {169} = 13 \\
 \]

Thus, the square root of 169 is 13.

5) We are given that the number is 225.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {225} = \sqrt {15 \times 15} \\
   \Rightarrow \sqrt {225} = 15 \\
 \]

Thus, the square root of 225 is 15.

6) We are given that the number is 324.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {324} = \sqrt {2 \times 2 \times 3 \times 3 \times 3 \times 3} \\
   \Rightarrow \sqrt {324} = 2 \times 3 \times 3 \\
   \Rightarrow \sqrt {324} = 18 \\
 \]

Thus, the square root of 324 is 18.

7) We are given that the number is 64.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {64} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 2} \\
   \Rightarrow \sqrt {64} = 2 \times 2 \times 2 \\
   \Rightarrow \sqrt {64} = 8 \\
 \]

Thus, the square root of 64 is 8.

8) We are given that the number is 121.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {121} = \sqrt {11 \times 11} \\
   \Rightarrow \sqrt {121} = 11 \\
 \]

Thus, the square root of 121 is 11.

9) We are given that the number is 361.
We will now find the square of the given number by finding the factors, we get\[
   \Rightarrow \sqrt {361} = \sqrt {19 \times 19} \\
   \Rightarrow \sqrt {361} = 19 \\
 \]
Thus, the square root of 361 is 19.

Note:
In this question, students should know that the square root of a number is a value that, when multiplied by itself, gives the number. This problem is really simple, students must follow the steps in order to find the required value. The square root of the number 121 can easily be calculated by multiplying 11 by itself.