Square root of 625 – Value and Derivation

In this article, we will learn about the square root of 625, its value and methods to derive it. Then we will solve some questions involving root 625 and learn the mathematical applications of square root.

We know that the value of square roots of perfect square numbers is very easy to find. Now, 625 is a perfect square number with 25 as its square root. The square root of 625 is expressed or represented as √625 in the radical form in mathematics. Another form of expressing the square root includes the exponential form, i.e., (625)^½ or (625)^0.5.

What is the value of √625?

In mathematics, we get the square of a number by multiplication of the number by itself. This is also known as raising a number to the power of 2. If x is a number, its square will be equal to x raised to the power 2, i.e., x².

Now, we know that 25 x 25 = 625, so the value of √625 is 25. This also has a negative value, but we will only consider the positive value.

How to find the value of the square root of 625 by prime factorisation?

To find the value of √625 by prime factorisation, follow the steps mentioned below:

1. First, calculate the prime factors of 625 and write them down.
   625 = 5 x 5 x 5 x 5
2. Group these prime factors in a pair of two factors each.
   625 = 5² x 5²
3. Add a square root on both sides.
   √625 = √(5² x 5²)
   √625 = √(5 x 5)²
    √625 = (5 x 5)^{2 x ½}
   √625 = 25

In a similar way the square root of 625 can also be written as -25. The mathematical form:  (-25) x (-25) =625. As the product of two(or even number) of negatives yields a positive value.

Finding the value of root 625 by long division

1. As shown in the image, write 625. Start by placing a bar above it, grouping the number in pairs of two digits from the right. The left unpaired number can be regarded as a single entity. For instance, for the number 625, 25 has one bar above it, and 6 has the second.
2. We know that digit 2’s square root is 4. Therefore, given that 2 is the quotient and divisor, the remainder equals 2.
3. Now, we’re going to bring down the next two numbers as a dividend, i.e. 25, and add 2 to our next divisor, i.e. 2+2 =4.
4. Select a number for the unit place of the divisor to yield 225 or a smaller number closest to 225 when multiplied by the new divisor. The number is 45 since 45 x 5 = 225 here.
5. Since the final remainder is zero, the two-digit quotient we get is 25 and it is the final value, i.e, square root of 625.

Is root 625 rational or irrational?

625 is the perfect square of +25 and -25. Both of which can be represented in the form of p/q. Where p and q are integers and q is not equal to 0.

Therefore √625 is a rational number.

Table of the square root of numbers from 1 to 50

The table below gives the value (positive) of square roots from 1 to 50 up to 3 decimal places. Keep it handy while solving mathematical problems.

Solved examples

Question 1: What will the radius of a circle be if its area is given as  625π cm²

Solution : Given, the area of the circle = 625π cm²

Now, area = πr²

So,

πr² = 625π cm²

We get, r² = 625 cm²

r = √625 cm²

Putting the value of √625 in the above equation,

We get, r = 25 cm

Therefore, the radius of the circle is 25 cm.

Question 2: Simplify √81 + √625 – √144. (Note that all values of square roots will be positive)

Solution: Given, √81 + √625 – √144

We know that √81 = +9, √144 = +12  and √625 = +25

Putting these square root values in the equation

We get, 9 + 25 – 12 = 22

So,  √81 + √625 – √144 upon simplification gives 22.