Using the prime factor method find the square root of 31.36

Usinng the prime factor method square root of31.36 is 5.6

Math

To find the square root of 31.36 using the prime factorization method, follow these steps:

Step 1: Write the number 31.36 as a product of its prime factors.
To do this, divide 31.36 by the smallest prime number, which is 2:
31.36 ÷ 2 = 15.68

Next, divide 15.68 by 2 again:
15.68 ÷ 2 = 7.84

Continue dividing by 2 until you can't divide anymore:
7.84 ÷ 2 = 3.92

Now, divide by the next prime number, which is 3:
3.92 ÷ 3 = 1.307

Since 1.307 is not divisible by any prime number, we have completed the prime factorization of 31.36:
31.36 = 2^5 × 3^1 × 1.307^1

Step 2: Split the prime factors into pairs of the same base, with one factor from each pair outside the square root:
√(31.36) = √(2^5 × 3^1 × 1.307^1)

Splitting the prime factors:
√(2^4 × 2^1 × 3^0 × 3^1 × 1.307^1)

Step 3: Rewrite the square root using the exponent property:
√(2^4) × √(2^1) × √(3^0) × √(3^1) × √(1.307^1)

Step 4: Simplify the square roots:
2^2 × √2 × 3^0 × √3 × 1.307^0.5

Step 5: Simplify the exponents:
4 × 2 × 1 × √3 × 1.307^0.5

Step 6: Multiply the numbers outside the square root:
8 × √3 × 1.307^0.5

Step 7: Calculate the value of the square root:
8 × √3 × 1.26 ≈ 8 × 1.732 ≈ 13.856

Therefore, the square root of 31.36 is approximately 13.856.

To find the square root of 31.36 using the prime factor method, follow these steps:

Step 1: Prime factorize the number 31.36.
- Start by dividing the number by the smallest prime number, which is 2.
- 31.36 ÷ 2 = 15.68
- Since 15.68 is not a whole number, try dividing it by 2 again.
- 15.68 ÷ 2 = 7.84
- Continue dividing by the smallest prime until you can no longer divide evenly.

Step 2: Write the prime factors in pairs.
- The prime factors of 31.36 are 2, 2, 2, 2, 2, and 7.
- Write them in pairs: 2^5 * 7.

Step 3: Take half of each pair of 2's and multiply them separately.
- Take half of the exponent of 2, which is 5 divided by 2 = 2.
- Multiply this by the base, 2, as well as any other primes that are not part of the pair.
- (2^2) * 2 * 7 = 28.

Therefore, the square root of 31.36 is √31.36 = √(2^2 * 2 * 7) = 2√(2 * 7) = 2√14 ≈ 5.92