The square root of 96 1/25 is calculated as follows: First, we need to simplify the mixed number 96 1/25. To do this, we multiply the whole number (96) by the denominator of the fraction (25) and add the numerator (1). This gives us 2401/25. Next, we can find the square root of 2401/25. To simplify the fraction, we can take the square root of the numerator (2401) and the square root of the denominator (25) separately. The square root of 2401 is 49, and the square root of 25 is 5. Therefore, the square root of 96 1/25 is equal to 49/5.
The Correct Answer and Explanation is:
To find the square root of the mixed number 9612596 \frac{1}{25}96251, we need to follow a few steps to simplify and compute the square root.
Step 1: Convert the mixed number to an improper fraction.
A mixed number is made up of a whole number and a fraction. The first step is to convert the mixed number 9612596 \frac{1}{25}96251 into an improper fraction.
To do this:
- Multiply the whole number (96) by the denominator of the fraction (25), which gives 96×25=240096 \times 25 = 240096×25=2400.
- Then, add the numerator of the fraction (1) to this result: 2400+1=24012400 + 1 = 24012400+1=2401.
Thus, 9612596 \frac{1}{25}96251 becomes the improper fraction 240125\frac{2401}{25}252401.
Step 2: Take the square root of the improper fraction.
Now that we have 240125\frac{2401}{25}252401, we can take the square root of the numerator and the denominator separately:
- The square root of the numerator 240124012401 is 494949, because 492=240149^2 = 2401492=2401.
- The square root of the denominator 252525 is 555, because 52=255^2 = 2552=25.
Thus, the square root of 240125\frac{2401}{25}252401 is 495\frac{49}{5}549.
Step 3: Final answer.
The square root of 9612596 \frac{1}{25}96251 is 495\frac{49}{5}549, which is the simplified form of the square root of the mixed number.
Explanation:
By breaking down the mixed number into an improper fraction, we could easily compute the square root of both the numerator and the denominator. The result 495\frac{49}{5}549 is a simplified rational number that represents the square root of the original mixed number. This approach uses basic operations such as multiplication and addition to simplify the fraction, followed by extracting square roots from both parts of the fraction.
