Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 7/3.
The square root is the inverse of the square of a number. 7/3 is not a perfect square. The square root of 7/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(7/3), whereas (7/3)^(1/2) in the exponential form. √(7/3) approximately equals 1.5275, 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 the long division method and approximation method are used. Let us now learn the following methods:
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: Convert the fraction 7/3 into a decimal, approximately 2.333.
Step 2: To begin with, we need to group the numbers from right to left. In the case of 2.333, we need to group it as 2.33 and 0.03.
Step 3: Now we need to find n whose square is less than or equal to 2.33. We can choose n as ‘1’ because 1 × 1 is lesser than or equal to 2.33. Now the quotient is 1 and the remainder is 1.33.
Step 4: Bring down 0.03 to make it 133. Add the old divisor with the same number 1 + 1 to get 2 which will be our new divisor.
Step 5: The next step is finding 2n × n ≤ 133. Let us consider n as 6, now 26 × 6 = 156 which is more than 133, so we choose n as 5.
Step 6: Subtract 133 - 125 (25 × 5) to get 8 and the quotient is 1.5.
Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding a decimal point allows us to add two zeroes to the dividend. Now the new dividend is 800.
Step 8: Find the new divisor, which is 31, because 31 × 2 gives a number less than 80.
Step 9: Subtract 800 - 775 (31 × 25) to get the remainder 25.
Step 10: Continue these steps until you get two decimal places.
The square root of √(7/3) is approximately 1.5275.
The approximation method is another method for finding square roots, and 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 7/3 using the approximation method.
Step 1: Convert 7/3 into a decimal, approximately 2.333.
Step 2: Find the closest perfect squares around 2.333. The smallest perfect square is 1 and the largest is 4. √(7/3) falls somewhere between 1 and 2.
Step 3: Apply the interpolation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).Going by the formula: (2.333 - 1) / (4 - 1) = 0.444.
Step 4: Using the formula, we identify the decimal point of our square root. Adding this to the smallest integer, 1 + 0.444 = 1.444, so the square root of 7/3 is approximately 1.5275.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √(7/3)?
The area of the square is approximately 2.333 square units.
The area of the square = side².
The side length is given as √(7/3).
Area of the square = (√(7/3))² = 7/3 ≈ 2.333.
Therefore, the area of the square box is approximately 2.333 square units.
A square-shaped plot measuring 7/3 square feet is built; if each of the sides is √(7/3), what will be the square feet of half of the plot?
Approximately 1.1665 square feet
We can divide the given area by 2 as the plot is square-shaped.
Dividing 7/3 by 2 = 7/6 ≈ 1.1665.
So half of the plot measures approximately 1.1665 square feet.
Calculate √(7/3) × 5.
7.6375
The first step is to find the square root of 7/3, which is approximately 1.5275.
The second step is to multiply 1.5275 by 5.
So 1.5275 × 5 = 7.6375.
What will be the square root of (7/3 + 1)?
The square root is approximately 1.8257.
To find the square root, we need to find the sum of (7/3 + 1).
7/3 + 1 = 10/3, and then √(10/3) ≈ 1.8257.
Therefore, the square root of (7/3 + 1) is approximately 1.8257.
Find the perimeter of a rectangle if its length 'l' is √(7/3) units and the width 'w' is 3 units.
We find the perimeter of the rectangle as 9.055 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(7/3) + 3) = 2 × (1.5275 + 3) = 2 × 4.5275 = 9.055 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.
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