Last updated on May 26th, 2025
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 695.
The square root is the inverse of the square of the number. 695 is not a perfect square. The square root of 695 is expressed in both radical and exponential form. In the radical form, it is expressed as √695, whereas (695)^(1/2) in the exponential form. √695 ≈ 26.366, which is an irrational number because it cannot 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. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:
The product of prime factors is the prime factorization of a number. Now let us look at how 695 is broken down into its prime factors:
Step 1: Finding the prime factors of 695
Breaking it down, we get 5 x 139, which means 695 = 5^1 x 139^1
Step 2: Now we found out the prime factors of 695. The second step is to make pairs of those prime factors. Since 695 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating √695 using prime factorization is not feasible.
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. 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 695, we need to group it as 6 and 95.
Step 2: Now we need to find n whose square is ≤ 6. We can say n is ‘2’ because 2 x 2 = 4, which is less than 6. Now the quotient is 2 after subtracting 4 from 6, the remainder is 2.
Step 3: Bring down the next pair, 95, making the new dividend 295.
Step 4: Double the quotient obtained (2) to get the new divisor, 4.
Step 5: Find a digit, say ‘x,’ such that 4x * x ≤ 295. The correct x is 6, since 46 * 6 = 276.
Step 6: Subtract 276 from 295, and the remainder is 19.
Step 7: Since the dividend is smaller than the divisor, we need to add a decimal point, allowing us to bring down two zeroes, making the new dividend 1900.
Step 8: The new divisor now becomes 526 (adding 6 to 46 and appending a digit), and we find an x such that 526x * x ≤ 1900. The correct x is 3, since 526 * 3 = 1578.
Step 9: Continue these steps until you have the desired level of precision. The square root of 695 is approximately 26.366.
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 695 using the approximation method.
Step 1: Identify the closest perfect squares. The closest perfect square less than 695 is 676 and the one greater is 729. √695 falls somewhere between 26 and 27.
Step 2: Use the formula: (Given number - smaller perfect square) ÷ (Greater perfect square - smaller perfect square). (695 - 676) ÷ (729 - 676) = 19 ÷ 53 ≈ 0.358
Step 3: Add this decimal to the smaller square root: 26 + 0.358 = 26.358 Thus, the square root of 695 is approximately 26.358.
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √695?
The area of the square is approximately 695 square units.
The area of the square = side^2.
The side length is given as √695.
Area of the square = side^2 = (√695) x (√695) = 695.
Therefore, the area of the square box is approximately 695 square units.
A square-shaped building measuring 695 square feet is built; if each of the sides is √695, what will be the square feet of half of the building?
347.5 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 695 by 2 = we get 347.5.
So half of the building measures 347.5 square feet.
Calculate √695 × 5.
131.83
The first step is to find the square root of 695, which is approximately 26.366.
The second step is to multiply 26.366 by 5.
So 26.366 × 5 ≈ 131.83.
What will be the square root of (695 + 4)?
The square root is 26.73
To find the square root, we need the sum of (695 + 4). 695 + 4 = 699, and the square root of 699 is approximately 26.73.
Therefore, the square root of (695 + 4) is approximately 26.73.
Find the perimeter of the rectangle if its length ‘l’ is √695 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 129.73 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√695 + 38) = 2 × (26.366 + 38) = 2 × 64.366 = 129.73 units.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.