Square roots and irrational numbers practice
A. Find the square root of 25.
Answer: The square root of 25 is 5.
Sure! I can help you with practice problems involving square roots and irrational numbers. Here are a few examples:
Problem 1: Simplify the square root of 12.
Solution: To start, we can look for perfect square factors of 12, which are 4 and 2. We rewrite the square root of 12 as the square root of 4 times the square root of 3. The square root of 4 is 2, so the simplified form is 2√3.
Problem 2: Evaluate √45.
Solution: We can also simplify square roots using prime factors. The prime factorization of 45 is 3 * 3 * 5. We can rewrite √45 as √(3 * 3 * 5). The square root of 3 * 3 simplifies to 3, so the simplified form is 3√5.
Problem 3: Determine if √64 is a rational or irrational number.
Solution: The square root of 64 is 8, which is a whole number. Since it can be expressed as a ratio of two integers, 8 is a rational number.
Problem 4: Is √2 an irrational number? Explain.
Solution: Yes, √2 is an irrational number. An irrational number cannot be expressed as a fraction or a ratio of two integers. The square root of 2 cannot be simplified to a fraction, so it is considered irrational.
I hope these examples help you practice square roots and irrational numbers. Let me know if you have any more questions!