What is the square root of 1875?
Understand the Problem
The question is asking for the square root of 1875, which is a mathematical operation that can be solved through simplification or calculation.
Answer
$25\sqrt{3}$
Answer for screen readers
The exact answer is $25\sqrt{3}$.
Steps to Solve
- Prime Factorization of 1875
To simplify the square root, we first find the prime factors of 1875.
1875 is divisible by 5: $$ 1875 \div 5 = 375 $$
375 is also divisible by 5: $$ 375 \div 5 = 75 $$
75 is again divisible by 5: $$ 75 \div 5 = 15 $$
15 is divisible by 5: $$ 15 \div 5 = 3 $$
Now we have the factors: $$ 1875 = 5^4 \times 3^1 $$
- Applying the Square Root Property
Next, we apply the square root properties. The square root of a product can be written as the product of the square roots: $$ \sqrt{1875} = \sqrt{5^4 \times 3^1} = \sqrt{5^4} \times \sqrt{3^1} $$
- Calculating the Square Roots
Now we can calculate each square root:
$$ \sqrt{5^4} = 5^2 = 25 $$
$$ \sqrt{3^1} = \sqrt{3} $$
So, we have: $$ \sqrt{1875} = 25\sqrt{3} $$
- Final Calculation
If needed, we can approximate $\sqrt{3} \approx 1.732$. Therefore, $$ \sqrt{1875} \approx 25 \times 1.732 = 43.3 $$
The exact answer is $25\sqrt{3}$.
More Information
The square root of 1875 is simplified to $25\sqrt{3}$. If needed, this can be approximated to about 43.3, but keeping it in the simplest radical form is generally preferred in mathematics.
Tips
Common mistakes include:
- Forgetting to factor out all prime factors completely.
- Not applying the square root properties correctly.
- Rounding the square root approximation prematurely when an exact form is required.
