What is the square root of 12100?
Understand the Problem
The question is asking for the square root of 12100. To find this, we will look for a number that when multiplied by itself equals 12100.
Answer
The square root of 12100 is $110$.
Answer for screen readers
The square root of 12100 is $110$.
Steps to Solve
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Identify the problem We need to find the square root of 12100. This can be expressed as: $$ \sqrt{12100} $$
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Factor the number To find the square root, we can factor 12100. We start by dividing it by smaller prime numbers. 12100 is even, so we can divide by 2: $$ 12100 \div 2 = 6050 $$
Continuing to factor: $$ 6050 \div 2 = 3025 $$ Now we will factor 3025 by trying small numbers. $$ 3025 \div 5 = 605 $$ $$ 605 \div 5 = 121 $$ $$ 121 \div 11 = 11 $$ $$ 11 \div 11 = 1 $$ Thus, the prime factorization of 12100 is: $$ 2^2 \times 5^2 \times 11^2 $$
- Apply square root to the factors Now, we can take the square root of each factor: $$ \sqrt{12100} = \sqrt{2^2 \times 5^2 \times 11^2} $$ Using the property of square roots: $$ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} $$
We now have: $$ \sqrt{2^2} \times \sqrt{5^2} \times \sqrt{11^2} = 2 \times 5 \times 11 $$
- Calculate the result Now, we can calculate: $$ 2 \times 5 = 10 $$ $$ 10 \times 11 = 110 $$
Thus, the square root of 12100 is: $$ 110 $$
The square root of 12100 is $110$.
More Information
Finding the square root by prime factorization simplifies the process, especially for larger numbers, as it allows us to break the number down into manageable parts. The process can be visually represented, which also helps in understanding.
Tips
- Ignoring prime factorization: Many might try to guess the square root without factoring, leading to errors. Always check your factors.
- Overlooking negative roots: While we often look for the principal square root, remember that a quadratic equation has two possible roots (positive and negative).
