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Last updated on April 8th, 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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 358.
The square root is the inverse of the square of a number. 358 is not a perfect square. The square root of 358 is expressed in both radical and exponential form. In radical form, it is expressed as √358, whereas (358)^(1/2) in exponential form. √358 ≈ 18.9209, 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 product of prime factors is the prime factorization of a number. Now let us look at how 358 is broken down into its prime factors.
Step 1: Finding the prime factors of 358 Breaking it down, we get 2 x 179: 2^1 x 179^1
Step 2: Now we found the prime factors of 358. Since 358 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 358 using prime factorization is impractical for finding the square root.
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 358, we need to group it as 58 and 3.
Step 2: Now we need to find n whose square is less than or equal to 3. We can say n is ‘1’ because 1 x 1 is lesser than or equal to 3. The quotient is 1, and after subtracting 1 from 3, the remainder is 2.
Step 3: Now let us bring down 58, making it the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 258. Consider n as 9, now 29 x 9 = 261, which is greater than 258, so we use n as 8. 28 x 8 = 224.
Step 6: Subtract 224 from 258; the difference is 34, and the quotient is 18.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3400.
Step 8: Now we need to find the new divisor that is 189 because 1890 x 9 = 3402, which is too large, so we use 188 instead. 1880 x 8 = 1504.
Step 9: Subtracting 1504 from 3400 gives us a remainder. The quotient now is 18.9.
Step 10: Continue these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue till the remainder is zero.
So the square root of √358 is approximately 18.92.
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 358 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √358. The closest perfect square less than 358 is 324 (18^2), and the closest perfect square greater than 358 is 361 (19^2). √358 falls between 18 and 19.
Step 2: Now we need to apply the formula that is
(Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).
Going by the formula (358 - 324) ÷ (361-324) = 34 ÷ 37 ≈ 0.919.
Using the formula, we identified the decimal point of our square root.
The next step is adding the initial integer value to the decimal number, which is 18 + 0.919 = 18.919, so the approximate square root of 358 is 18.92.
Can you help Max find the area of a square box if its side length is given as √358?
A square-shaped building measuring 358 square feet is built; if each of the sides is √358, what will be the square feet of half of the building?
Calculate √358 × 5.
What will be the square root of (338 + 20)?
Find the perimeter of the rectangle if its length ‘l’ is √358 units and the width ‘w’ is 38 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.