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

  1. Simplify the radicand (number inside the square root)

    Break down 288 into its prime factors: $$288 = 2^5 imes 3^2$$

    1. 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.

    1. Take one number from each pair outside the square root

    For each pair of factors, take one outside the square root: $$\sqrt{288} = \sqrt{(2^2 imes 2^2 imes 2) imes 3^2} = 2 imes 2 imes 3 \sqrt{2}$$

    1. 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.

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