129 LearnersLast updated on May 26th, 2025
Square Root of 348
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 348.
What is the Square Root of 348?
The square root is the inverse of squaring a number. 348 is not a perfect square. The square root of 348 can be expressed in both radical and exponential form. In radical form, it is expressed as √348, whereas in exponential form it is expressed as (348)^(1/2). √348 ≈ 18.65475, which is an irrational number because it cannot be expressed as a ratio of two integers.
Finding the Square Root of 348
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like the long division method and approximation method are used. Let's learn these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 348 by Prime Factorization Method
Prime factorization involves expressing a number as a product of its prime factors. Here's how we break down 348 into its prime factors:
Step 1: Find the prime factors of 348. Breaking it down, we get 2 x 2 x 3 x 29: 2^2 x 3^1 x 29^1
Step 2: We found the prime factors of 348. Since 348 is not a perfect square, the digits cannot be grouped into pairs for exact calculation, making prime factorization insufficient for exact square root calculation.
Square Root of 348 by Long Division Method
The long division method is useful for non-perfect square numbers. This method involves finding the closest perfect squares. Let's see how to find the square root using long division, step by step:
Step 1: Group the numbers from right to left. For 348, group as 48 and 3.
Step 2: Find n such that n^2 is ≤ 3. Here, n = 1 since 1^2 ≤ 3. Subtract 1 from 3, remainder is 2.
Step 3: Bring down the next pair to get 248. Double the divisor (1 + 1 = 2) to form a new divisor.
Step 4: Find n such that 2n x n ≤ 248. Choose n as 8, since 28 x 8 = 224.
Step 5: Subtract 224 from 248, remainder is 24.
Step 6: Bring down the next pair (00) to form 2400. Add a decimal point to quotient.
Step 7: Find the new divisor as 289. Calculate 289 x 8 = 2312.
Step 8: Subtract 2312 from 2400, remainder is 88.
Step 9: Continue the steps until desired precision. Quotient is approximately 18.65.
Square Root of 348 by Approximation Method
The approximation method is a straightforward way to find square roots. Here's how to approximate the square root of 348:
Step 1: Identify the nearest perfect squares surrounding 348. The closest perfect squares are 324 (18^2) and 361 (19^2). √348 lies between 18 and 19.
Step 2: Apply the formula: (Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square). (348 - 324) ÷ (361 - 324) = 24 ÷ 37 ≈ 0.6486 Add this decimal to the smaller base: 18 + 0.6486 = 18.6486. So, the square root of 348 ≈ 18.65.
Common Mistakes and How to Avoid Them in the Square Root of 348
Students often make mistakes in finding square roots, such as forgetting the negative square root or skipping important steps like the long division method. Let's review some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's essential for students to remember that numbers have both positive and negative square roots. In most practical situations, we consider only the positive square root.
For example, √50 = 7.07, but there's also -7.07, which is often overlooked.
Mistake 2
Not adding square root symbols in proper places
Incorrect placement of square root symbols is a common error. It's important to simplify numbers within the square root first.
For example, √(12 + 24) ≠ √12 + √24. The correct simplification is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify numbers inside the square root to avoid errors in approximation.
For example, √50 ≠ 7; the correct value is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students must distinguish between square root and cube root symbols to avoid confusion.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
The long division method for square roots involves many steps, and missing a step can result in errors. It's crucial to follow each step carefully to reach the correct answer.
Square Root of 348 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √348?
The area of the square is approximately 348 square units.
Explanation
The area of a square = side².
Given side length is √348.
Area = (√348)² = 348 square units.
Therefore, the area is approximately 348 square units.
Problem 2
A square-shaped building measuring 348 square feet is built; if each side is √348, what will be the square feet of half of the building?
174 square feet
Explanation
Since the building is square-shaped, divide the total area by 2 to find half the area. 348 ÷ 2 = 174
Thus, half of the building measures 174 square feet.
Problem 3
Calculate √348 x 5.
Approximately 93.27
Explanation
First, find the square root of 348, approximately 18.65.
Multiply 18.65 by 5. 18.65 x 5 ≈ 93.27
Problem 4
What will be the square root of (348 + 4)?
The square root is 19.
Explanation
Calculate the sum: 348 + 4 = 352. Find the square root of 352: √352 ≈ 18.76.
Therefore, the square root of (348 + 4) is approximately ±18.76.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √348 units and the width 'w' is 38 units.
The perimeter is approximately 113.3 units.
Explanation
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√348 + 38) = 2 × (18.65 + 38) ≈ 2 × 56.65 ≈ 113.3 units.
FAQ on Square Root of 348
1.What is √348 in its simplest form?
2.Mention the factors of 348.
3.Calculate the square of 348.
4.Is 348 a prime number?
5.348 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 348?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 348?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 348
- Square root: A square root is the inverse operation of squaring. For example, if 4^2 = 16, then √16 = 4.
- Irrational number: An irrational number cannot be expressed as a ratio of two integers.
- Perfect square: A perfect square is an integer that is the square of another integer.
- Prime factorization: Expressing a number as a product of its prime numbers.
- Long division method: A method used to find the square root of non-perfect square numbers by dividing and averaging.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
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