What is the square root of 5775

What is the square root of 5775? Solve it.

The correct answer and explanation is:

Correct Answer:

The square root of 5775 is approximately 75.999, or √5775 ≈ 76 (rounded to the nearest whole number).

Explanation:

To find the square root of 5775, first recognize that this number is not a perfect square. A perfect square is a number that can be expressed as the square of an integer, like 64 (which is 8 × 8) or 121 (which is 11 × 11). Since 5775 is not a perfect square, its square root will be a non-integer (a decimal value).

Step-by-step estimation method:

1. Find two perfect squares between which 5775 lies:
   • 752=562575^2 = 5625
   • 762=577676^2 = 5776
   Since 5775 is between 5625 and 5776, it means: 75<5775<7675 < \sqrt{5775} < 76
2. Try calculating with decimals to get a more accurate value:
   • 75.92=5766.8175.9^2 = 5766.81
   • 75.952=5771.402575.95^2 = 5771.4025
   • 75.992=5774.640175.99^2 = 5774.6401
   • 76.02=577676.0^2 = 5776
   So, 5775≈75.999\sqrt{5775} \approx 75.999

This value is very close to 76, and rounding it gives the nearest whole number as 76.

Application and significance:

Knowing how to estimate or calculate the square root of a non-perfect square like 5775 is useful in both academics and real life. In subjects such as physics, engineering, and construction, square roots appear in formulas related to area, speed, distance, energy, and much more.

In many cases, the square root may not be a whole number. When this happens, the result can be expressed in decimal form for precision or as a simplified radical if exactness is needed. For 5775, because it is not a perfect square and cannot be simplified easily into a product of perfect squares, the decimal form is the most practical and precise representation.

In conclusion, the square root of 5775 is approximately 75.999.