What is the square root of 288?
Understand the Problem
The question is asking to calculate the square root of 288, which is a mathematical operation involving finding a number that, when multiplied by itself, equals 288.
Answer
12√2
Answer for screen readers
The final answer is 12√2
Steps to Solve
-
Simplify the radicand (number inside the square root)
Break down 288 into its prime factors: $$288 = 2^5 imes 3^2$$
- Pair the prime factors
Identify pairs of prime factors: $$2^5$$ has two pairs of 2's and one leftover 2, $$3^2$$ has one pair of 3's.
- Take one number from each pair outside the square root
For each pair of factors, take one outside the square root: $$\sqrt{288} = \sqrt{(2^2 imes 2^2 imes 2) imes 3^2} = 2 imes 2 imes 3 \sqrt{2}$$
- Simplify the expression
Multiply the numbers outside the square root: $$\sqrt{288} = 12\sqrt{2}$$
The final answer is 12√2
More Information
Square roots are fundamental in various mathematical domains, including geometry and algebra.
Tips
A common mistake is forgetting to simplify the square root fully by not factoring the number completely or by not identifying pairs correctly.
