What is the square root of 61
The Correct Answer and Explanation is:
Square Root of 61
The square root of 61 is approximately:
√61 ≈ 7.810249675906654
This is an irrational number, meaning it cannot be expressed as an exact fraction and its decimal form goes on infinitely without repeating.
Explanation
The square root of a number is a value that, when multiplied by itself, gives the original number. So, the square root of 61 is the number that satisfies this equation: x2=61x^2 = 61
61 is not a perfect square, like 49 (which is 7²) or 64 (which is 8²), so its square root isn’t a whole number. Since 61 lies between 49 and 64, we know that: 72=49and82=647^2 = 49 \quad \text{and} \quad 8^2 = 64
Therefore, √61 lies between 7 and 8. To get a more accurate value, we can use long division method, Newton’s method, or a calculator. Using these methods, we find: 61≈7.810249675906654\sqrt{61} ≈ 7.810249675906654
Because the decimal neither ends nor repeats, √61 is classified as an irrational number. Irrational numbers like √2, √3, and √61 cannot be exactly written as a ratio of two integers.
Despite being irrational, square roots like √61 are important in geometry, algebra, and real-world applications. For example, if a square has an area of 61 square units, then each side of the square would be √61 units long.
In math problems, we often round irrational roots to a desired number of decimal places. For most purposes, rounding to two decimal places is sufficient: 61≈7.81\sqrt{61} ≈ 7.81
In conclusion, the square root of 61 is an irrational number that lies between 7 and 8 and is approximately equal to 7.81. It’s useful in both theoretical mathematics and practical applications involving measurement or geometry.
