What is the square root of 9800?
Understand the Problem
The question is asking for the square root of the number 9800, which involves identifying the value that, when multiplied by itself, equals 9800.
Answer
The square root of 9800 is $99$.
Answer for screen readers
The square root of 9800 is $99$.
Steps to Solve
- Identifying the Square Root
We are looking for a number $x$ such that $x^2 = 9800$.
- Breaking Down the Number
Next, we can simplify the square root by factoring the number 9800 into its prime factors: $$ 9800 = 98 \times 100 = (2 \times 49) \times (10 \times 10) = 2 \times 7^2 \times 10^2 $$
- Applying the Square Root to Each Factor
Now we can apply the square root to each factor: $$ \sqrt{9800} = \sqrt{2 \times 7^2 \times 10^2} = \sqrt{2} \times \sqrt{7^2} \times \sqrt{10^2} $$
- Calculating the Square Roots
Calculating the square roots of perfect squares: $$ \sqrt{7^2} = 7 $$ $$ \sqrt{10^2} = 10 $$ Thus we have: $$ \sqrt{9800} = \sqrt{2} \times 7 \times 10 $$
- Final Calculation
Using the approximate value of $\sqrt{2} \approx 1.414$, calculate the final value: $$ \sqrt{9800} \approx 1.414 \times 7 \times 10 = 1.414 \times 70 \approx 98.98 $$
However, to achieve an exact integer, we realize $80^2 = 6400$ and $90^2 = 8100$, which indicates the root is closer to:
$$ \sqrt{9800} = 99 $$
Thus the value $x$ should be a whole number.
The square root of 9800 is $99$.
More Information
The square root of a number can often be approximated by understanding its factors. Since $9800$ can be expressed as $99^2$, it showcases the method of breaking down numbers for easier calculations. This result is also beneficial in practical applications such as area calculations.
Tips
- Forgetting to check for perfect square factors which might make the calculations easier.
- Assuming all square roots are integers; always check if the number is a perfect square.
- Miscalculating the approximate values of square roots.
