The Correct Answer and Explanation is:
The correct answer is 127.65.
The problem asks to simplify the expression presented in the image. Correcting the spelling, the expression is:
Square root of 13225 + Square root of 132.25 + Square root of 1.3225.
In mathematical notation, this is written as:
√13225 + √132.25 + √1.3225
To find the solution, we can calculate each square root term separately and then sum the results.
First, we find the square root of 13225. A helpful observation is that the number ends in 25, which means its square root must end in 5. We can find the value by testing or by recognizing the pattern. The square root of 13225 is 115, because 115 × 115 = 13225.
So, √13225 = 115.
Next, we calculate the square root of 132.25. We can see a relationship between this number and the first one. The number 132.25 is equal to 13225 divided by 100. This relationship allows for a simpler calculation of its square root:
√132.25 = √(13225 / 100)
Using the property of square roots where √(a/b) = √a / √b, we get:
√13225 / √100 = 115 / 10 = 11.5.
So, √132.25 = 11.5.
For the third term, we find the square root of 1.3225. This number is equal to 13225 divided by 10000. We apply the same method as before:
√1.3225 = √(13225 / 10000)
√13225 / √10000 = 115 / 100 = 1.15.
So, √1.3225 = 1.15.
Finally, to get the final answer, we add the three values we calculated:
115 + 11.5 + 1.15
Adding these numbers together, we get:
115.00
11.50
- 1.15
127.65
Thus, the simplified value of the expression is 127.65.
