Find the square root of 25/4.
The correct answer and explanation is:
The square root of 254\frac{25}{4} can be simplified by taking the square root of both the numerator and the denominator separately.
Step-by-step solution:
- Break the fraction into two parts: 254=254\sqrt{\frac{25}{4}} = \frac{\sqrt{25}}{\sqrt{4}}.
- The square root of 25 is 5, because 5×5=255 \times 5 = 25.
- The square root of 4 is 2, because 2×2=42 \times 2 = 4.
- Therefore, 254=52\frac{\sqrt{25}}{\sqrt{4}} = \frac{5}{2}.
Final Answer:
The square root of 254\frac{25}{4} is 52\frac{5}{2} or 2.5.
Explanation:
When finding the square root of a fraction, the key is to take the square root of both the numerator and the denominator separately. The square root operation is the inverse of squaring a number. For instance, the square root of 25 is 5 because squaring 5 results in 25. Similarly, the square root of 4 is 2 because squaring 2 results in 4.
It is important to note that the square root of a fraction is equal to the fraction of the square roots, meaning you take the square root of the numerator and denominator separately. In this case, the numerator is 25 and the denominator is 4. Taking the square root of both gives you 5 for the numerator and 2 for the denominator. Thus, the simplified result is 52\frac{5}{2}, which is equivalent to 2.5.
Understanding this concept can be very useful in various mathematical calculations, including when working with ratios, proportions, and solving algebraic problems.