Square Root / FREE Printable Worksheets - Worksheetfun - Free Printable

To solve the problem of finding the square roots of the given numbers, we will calculate each one step by step. Let's go through each number:

1. $\sqrt{12100}$

- We need to find a number $x$ such that $x^2 = 12100$.
- Notice that $12100 = 121 \times 100$.
- The square root of $121$ is $11$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{12100} = \sqrt{121} \times \sqrt{100} = 11 \times 10 = 110$.

2. $\sqrt{8900}$

- This number does not have an exact integer square root. We can approximate it using a calculator.
- Using a calculator, $\sqrt{8900} \approx 94.34$.

3. $\sqrt{40000}$

- We need to find a number $x$ such that $x^2 = 40000$.
- Notice that $40000 = 400 \times 100$.
- The square root of $400$ is $20$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{40000} = \sqrt{400} \times \sqrt{100} = 20 \times 10 = 200$.

4. $\sqrt{36100}$

- We need to find a number $x$ such that $x^2 = 36100$.
- Notice that $36100 = 361 \times 100$.
- The square root of $361$ is $19$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{36100} = \sqrt{361} \times \sqrt{100} = 19 \times 10 = 190$.

5. $\sqrt{22500}$

- We need to find a number $x$ such that $x^2 = 22500$.
- Notice that $22500 = 225 \times 100$.
- The square root of $225$ is $15$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{22500} = \sqrt{225} \times \sqrt{100} = 15 \times 10 = 150$.

6. $\sqrt{8100}$

- We need to find a number $x$ such that $x^2 = 8100$.
- Notice that $8100 = 81 \times 100$.
- The square root of $81$ is $9$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{8100} = \sqrt{81} \times \sqrt{100} = 9 \times 10 = 90$.

7. $\sqrt{10000}$

- We need to find a number $x$ such that $x^2 = 10000$.
- Notice that $10000 = 100 \times 100$.
- The square root of $100$ is $10$.
- Therefore, $\sqrt{10000} = \sqrt{100} \times \sqrt{100} = 10 \times 10 = 100$.

8. $\sqrt{16900}$

- We need to find a number $x$ such that $x^2 = 16900$.
- Notice that $16900 = 169 \times 100$.
- The square root of $169$ is $13$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{16900} = \sqrt{169} \times \sqrt{100} = 13 \times 10 = 130$.

9. $\sqrt{7200}$

- This number does not have an exact integer square root. We can approximate it using a calculator.
- Using a calculator, $\sqrt{7200} \approx 84.85$.

10. $\sqrt{32400}$

- We need to find a number $x$ such that $x^2 = 32400$.
- Notice that $32400 = 324 \times 100$.
- The square root of $324$ is $18$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{32400} = \sqrt{324} \times \sqrt{100} = 18 \times 10 = 180$.

11. $\sqrt{19600}$

- We need to find a number $x$ such that $x^2 = 19600$.
- Notice that $19600 = 196 \times 100$.
- The square root of $196$ is $14$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{19600} = \sqrt{196} \times \sqrt{100} = 14 \times 10 = 140$.

12. $\sqrt{25600}$

- We need to find a number $x$ such that $x^2 = 25600$.
- Notice that $25600 = 256 \times 100$.
- The square root of $256$ is $16$, and the square root of $100$ is $10$.
- Therefore, $\sqrt{25600} = \sqrt{256} \times \sqrt{100} = 16 \times 10 = 160$.

Final Answer:

\[
\boxed{
\begin{array}{ll}
\sqrt{12100} = 110 & \sqrt{8900} \approx 94.34 \\
\sqrt{40000} = 200 & \sqrt{36100} = 190 \\
\sqrt{22500} = 150 & \sqrt{8100} = 90 \\
\sqrt{10000} = 100 & \sqrt{16900} = 130 \\
\sqrt{7200} \approx 84.85 & \sqrt{32400} = 180 \\
\sqrt{19600} = 140 & \sqrt{25600} = 160 \\
\end{array}
}
\]