What is the square root of 784?

Steps to Solve

1. Identify the problem as finding a square root

We need to find the number that, when multiplied by itself, equals 784.

2. Use a calculator or factorization method

For exact results, you might use a calculator, or you can factorize. Start by breaking 784 down into prime factors.

$$784 \div 2 = 392$$ $$392 \div 2 = 196$$ $$196 \div 2 = 98$$ $$98 \div 2 = 49$$ $$49 \div 7 = 7$$ $$7 \div 7 = 1$$

So, the prime factorization of 784 is: $$784 = 2^4 \times 7^2$$

3. Apply the square root to the factorized form

We can take the square root of both sides: $$ \sqrt{784} = \sqrt{2^4 \times 7^2} $$

This can be simplified to: $$ \sqrt{784} = 2^2 \times 7 $$

So: $$ \sqrt{784} = 4 \times 7 $$

4. Calculate the final result

Perform the final multiplication: $$ 4 \times 7 = 28 $$