Please show me a step-by-step of square root of 2209 without using calculator or just say square root of 2209?
No ones going to answer man, the question is just kind of not worth answering since there is no step-by-step. Just tell your teacher you sat there multiplying pairs of numbers till you figured that 47^2=2209
Before calculators, we used a method similar to long division.
You will find it explained on this page
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
go about 1/4 down on the webpage to
"Finding square roots using an algorithm"
To find the square root of 2209 without using a calculator, you can use a method called "prime factorization" or "factor tree."
Step 1: Start by knowing that 2209 is a perfect square because it can be written as the product of two equal numbers. In this case, 47 is the square root of 2209, since 47 × 47 = 2209.
Step 2: Find the prime factors of 47.
Since 47 is a prime number, it cannot be factored any further. Therefore, 47 is already in its prime factorization form.
Step 3: Express the number 2209 as the multiplication of its prime factors.
2209 = 47 × 47
Step 4: Simplify and pair the prime factors in pairs of two.
Pairing 47 with itself, we have: √(47 × 47)
Step 5: Apply the property of square roots, which states that √(a × b) = √a × √b.
√(47 × 47) = √47 × √47
Step 6: Simplify the expression √47 × √47.
√47 × √47 = 47
Therefore, the square root of 2209 is 47.
Note: In practice, this method is useful for understanding how square roots are derived and to find the square root of numbers without a calculator. However, for larger numbers, prime factorization can be a time-consuming process, so using a calculator is often more efficient.