Square Root of 15625

The square root is the inverse of the square of a number. 15625 is a perfect square. The square root of 15625 is expressed in both radical and exponential form. In the radical form, it is expressed as √15625, whereas (15625)^(1/2) in the exponential form. √15625 = 125, 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. The long-division method and approximation method can also be used for verification. 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. Now let us look at how 15625 is broken down into its prime factors.

Step 1: Finding the prime factors of 15625 Breaking it down, we get 5 x 5 x 5 x 5 x 5 x 5: 5⁶

Step 2: Now we found the prime factors of 15625. The second step is to make pairs of those prime factors. Since 15625 is a perfect square, the digits of the number can be grouped in pairs.

Step 3: Taking one number from each pair gives us the square root: 5 x 5 x 5 = 125

The long division method can be used to find the square root of perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 15625, we need to group it as 15 625.

Step 2: Now we need to find n whose square is less than or equal to 15. We can say n is 3 because 3² = 9, which is less than 15. Now the quotient is 3, and the remainder is 15 - 9 = 6.

Step 3: Bring down the next pair of digits, 62, making the new dividend 662.

Step 4: Double the quotient and find the new divisor. The current quotient is 3, so doubling it gives us 6.

Step 5: We try 65 as the new divisor since 65 x 5 = 325, which is less than 662. The remainder is 662 - 325 = 337.

Step 6: Bring down the next pair of digits, 25, making the new dividend 33725.

Step 7: Double the current quotient (35) gives us 70. Step 8: Try 705 as the new divisor since 705 x 5 = 3525, which is less than 33725.

Step 9: The remainder is 33725 - 3525 = 0. So the square root of √15625 is 125.

Approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 15625 using the approximation method.

Step 1: Now we have to find the closest perfect square of √15625. Since 15625 is a perfect square, the square root is an integer.

Step 2: The square root is exactly 125, as calculated by methods above.

• Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root that is √16 = 4.

• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 16 is a perfect square since it is 4².

• Prime factorization: Prime factorization is expressing a number as the product of its prime factors. Example: 15625 = 5^6.