What is the square root of 4800?

Steps to Solve

1. 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 $2^5 \times 3^1 \times 5^2$.

2. Express the square root
   Next, we can express the square root of 4800 using its prime factors: $$ \sqrt{4800} = \sqrt{2^5 \times 3^1 \times 5^2} $$

3. Simplify the square root
   We can simplify the square root by taking the square root of each factor: $$ \sqrt{2^5} = 2^{5/2} = 2^2 \times \sqrt{2} = 4\sqrt{2} $$ $$ \sqrt{3^1} = 3^{1/2} = \sqrt{3} $$ $$ \sqrt{5^2} = 5^{2/2} = 5 $$

4. Combine the results
   Now we combine these results: $$ \sqrt{4800} = 4\sqrt{2} \times \sqrt{3} \times 5 $$ We can rearrange this: $$ \sqrt{4800} = 20\sqrt{6} $$