Square Root of 1343

The square root is the inverse of squaring a number. 1343 is not a perfect square. The square root of 1343 is expressed in both radical and exponential form. In radical form, it is expressed as √1343, whereas (1343)^(1/2) is the exponential form. √1343 ≈ 36.6508, 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:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 1343 is broken down into its prime factors:

Step 1: Finding the prime factors of 1343. Breaking it down, we get 1343 = 1 x 1343 (since 1343 is a prime number).

Step 2: Since 1343 is not a perfect square, it cannot be grouped into pairs. Therefore, calculating 1343 using prime factorization for finding a perfect square 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 1343, we need to group as 43 and 13.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n is 3 because 3 x 3 = 9. Now the quotient is 3, after subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 43, making the new dividend 443. Add the old divisor with the same number, 3 + 3 = 6, which will be our new divisor.

Step 4: Now we have 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 443. Let us consider n as 7, now 6 x 7 x 7 = 294.

Step 6: Subtract 294 from 443; the difference is 149, and the quotient is 37.

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 14900.

Step 8: Now we find the new divisor, which is 737. Continuing this way, the quotient builds, eventually reaching 36.6508.

So the square root of √1343 is approximately 36.6508.

Approximation method is another method for finding the 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 1343 using the approximation method:

Step 1: Now we have to find the closest perfect squares of √1343. The smallest perfect square less than 1343 is 1296 (36^2), and the largest perfect square greater than 1343 is 1369 (37^2). √1343 falls between 36 and 37.

Step 2: Now we need to apply the interpolation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1343 - 1296) ÷ (1369 - 1296) = 47 ÷ 73 ≈ 0.6438 Adding the integer part to this decimal gives us 36 + 0.6438 ≈ 36.6438, so the square root of 1343 is approximately 36.6438.

• Square root: A square root is the inverse of squaring a number. Example: 6² = 36, and the inverse of the square is the square root, which is √36 = 6.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

• Decimal: A decimal is a fraction written in a special form. Instead of writing 1/2, you can express it as 0.5.

• Approximation: An approximation is a value or quantity that is nearly but not exactly correct. It is often used for calculations involving irrational numbers.