Square Root of 90.25

The square root is the inverse of the square of the number. 90.25 is a perfect square. The square root of 90.25 is expressed in both radical and exponential form.

In the radical form, it is expressed as √90.25, whereas in the exponential form it is (90.25)^(1/2). The square root of 90.25 is 9.5, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. For non-perfect squares, methods such as the long-division method and approximation method are used. However, since 90.25 is a perfect square, we can directly find its square root. Let us now learn the following methods: -

1. Prime factorization method 
2. Long division method 
3. Approximation method

The product of prime factors is the prime factorization of a number. 90.25 is a perfect square and can be expressed as (9.5)^2.

Thus, the prime factorization method confirms that 90.25 is a perfect square, and its square root is 9.5.

The long division method can also be used for finding the square root of perfect squares. For 90.25, we can follow these steps:

Step 1: Group the numbers from right to left. For 90.25, we consider it as 90.25.

Step 2: Find a number whose square is closest to 90 without exceeding it. Here, that number is 9, because 9 × 9 = 81.

Step 3: Subtract 81 from 90, which gives 9. Bring down 25 to make it 925.

Step 4: Double the divisor (9) to get 18. Next, find a number n such that 18n × n is closest to 925 without exceeding it. Here, n is 5, because 185 × 5 = 925.

Step 5: Subtract 925 from 925, giving a remainder of 0. The quotient is 9.5.

So the square root of √90.25 is 9.5.

The approximation method is also an easy way to find the square root of a given number. Here, however, since 90.25 is a perfect square, we can directly approximate it as follows:

Step 1: Identify the number nearest to 90.25 that is a perfect square. Both 81 (9²) and 100 (10²) are near, but 90.25 is exactly 9.5².

Therefore, the square root of 90.25 is 9.5.

• Square root: A square root is the inverse of a square. Example: 9.5^2 = 90.25 and the inverse of the square is the square root, that is √90.25 = 9.5.

• Rational number: A rational number can be written in the form of p/q, where p and q are integers and q ≠ 0.

• Perfect square: A number that is the square of an integer is a perfect square. Example: 90.25 is a perfect square because it is 9.5² 

• Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. Example: 9.5 is a decimal.

• Principal square root: A number has both positive and negative square roots; however, the positive square root is often used in real-world applications and is known as the principal square root.