What is the square root of 640?
Understand the Problem
The question is asking for the square root of the number 640, which is a mathematical operation. We will identify the square root of this value, which can be done using various methods, including simplification and a calculator.
Answer
$8\sqrt{10}$
Answer for screen readers
The square root of 640 is $8\sqrt{10}$.
Steps to Solve
-
Identify the square root operation
The problem requires us to find the square root of 640, which is denoted as $\sqrt{640}$. -
Simplify the number 640
To simplify 640, we can factor it into its prime factors.
The prime factorization of 640 is:
$$ 640 = 2^7 \times 5^1 $$ -
Apply the square root property
We can use the property of square roots where $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to separate the factors:
$$ \sqrt{640} = \sqrt{(2^7) \times (5^1)} = \sqrt{2^6 \times 2^1 \times 5} $$ -
Calculate individual square roots
Now we can simplify further:
$$ \sqrt{640} = \sqrt{2^6} \times \sqrt{2^1} \times \sqrt{5} = 2^3 \times \sqrt{2} \times \sqrt{5} $$
This gives us:
$$ \sqrt{640} = 8\sqrt{10} $$ -
Final Result
Thus, the square root of 640 simplifies to $8\sqrt{10}$, which is our final answer.
The square root of 640 is $8\sqrt{10}$.
More Information
The number 640 can be represented as a product of primes, which allows us to simplify the square root operation. The result $8\sqrt{10}$ indicates both an integer part and an irrational part, which is common in square root calculations.
Tips
- Forgetting to simplify the square root and leaving it as $\sqrt{640}$ instead of breaking it down into prime factors.
- Miscalculating the square root of the perfect squares involved in the factorization.
