what is the square root of 900
The correct answer and explanation is:
The square root of 900 is 30.
Explanation:
To understand why the square root of 900 is 30, begin by considering the definition of a square root. A square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms:
$$
\sqrt{900} = x \quad \text{such that} \quad x \times x = 900
$$
Try the number 30:
$$
30 \times 30 = 900
$$
This confirms that 30 is the correct square root of 900.
Square roots are part of the broader family of radicals in mathematics. The symbol √ represents the principal (positive) square root. Every positive number actually has two square roots: one positive and one negative. For 900, those roots are +30 and -30. However, when people ask for “the square root,” they are usually referring to the principal, or positive, root.
The number 900 is a perfect square, which means it is the product of a whole number multiplied by itself. Perfect squares are important in arithmetic, algebra, and geometry. They help simplify equations, calculate distances, and analyze areas of square-shaped objects.
For example, in geometry, a square with side length 30 units will have an area of 900 square units. So if the area of a square is given as 900 square units, one can find the side length by taking the square root of 900, which is 30.
In real-life applications, square roots are used in fields like construction, engineering, physics, and finance. Understanding square roots is essential for solving quadratic equations, performing statistical calculations, and modeling physical systems.
In conclusion, the square root of 900 is 30 because 30 multiplied by itself equals 900. This result reflects a fundamental concept in mathematics involving perfect squares and their roots.