What is the square root of 4800?
Understand the Problem
The question is asking to find the square root of 4800, which is a mathematical operation requiring step-by-step calculation.
Answer
$20\sqrt{6}$
Answer for screen readers
The square root of 4800 is $20\sqrt{6}$.
Steps to Solve
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Factor the number
First, let's factor 4800 into its prime factors. We start by dividing by the smallest prime numbers:
- $4800 \div 2 = 2400$
- $2400 \div 2 = 1200$
- $1200 \div 2 = 600$
- $600 \div 2 = 300$
- $300 \div 2 = 150$
- $150 \div 2 = 75$
- $75 \div 3 = 25$
- $25 \div 5 = 5$
- $5 \div 5 = 1$
So, the prime factorization of $4800$ is $2^5 \times 3^1 \times 5^2$.
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Express the square root
Next, we can express the square root of 4800 using its prime factors: $$ \sqrt{4800} = \sqrt{2^5 \times 3^1 \times 5^2} $$ -
Simplify the square root
We can simplify the square root by taking the square root of each factor: $$ \sqrt{2^5} = 2^{5/2} = 2^2 \times \sqrt{2} = 4\sqrt{2} $$ $$ \sqrt{3^1} = 3^{1/2} = \sqrt{3} $$ $$ \sqrt{5^2} = 5^{2/2} = 5 $$ -
Combine the results
Now we combine these results: $$ \sqrt{4800} = 4\sqrt{2} \times \sqrt{3} \times 5 $$ We can rearrange this: $$ \sqrt{4800} = 20\sqrt{6} $$
The square root of 4800 is $20\sqrt{6}$.
More Information
The answer $20\sqrt{6}$ represents the exact square root of 4800. If you calculate this further, using a calculator, $20\sqrt{6}$ is approximately $48.99$.
Tips
- Forgetting to simplify the square root after factoring can lead to an incorrect answer.
- Miscalculating the powers of prime factors during tracing or simplifying the expression.
