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What is largest perfect square factor of 20?(1 point) Responses 5 5 20 20 4 4 1 1 Question 2 Simplify 20−−√ (1 point) Responses 45–√ 4square root of 5 25–√ 2square root of 5 210−−√ 2square root of 10 45–√ 4square root of 5 Question 3 Simplify 12−−√ (1 point) Responses 43–√ 4square root of 3 34–√ 3square root of 4 23–√ 2square root of 3 26–√

1 answer

Let's address each question one by one.

Question 1: What is the largest perfect square factor of 20?

  • To find the largest perfect square factor of 20, we can look at the factors of 20: 1, 2, 4, 5, 10, and 20. The perfect square factors are 1 and 4. The largest of these is 4.

Question 2: Simplify \( \sqrt{20} \).

  • We can simplify \( \sqrt{20} \) by breaking it down: \[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}. \] Thus, the simplified form is \( 2\sqrt{5} \).

Question 3: Simplify \( \sqrt{12} \).

  • Similarly, we can simplify \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}. \] So, the simplified form is \( 2\sqrt{3} \).

Here's a summary of the answers:

  1. Largest perfect square factor of 20: 4
  2. Simplified \( \sqrt{20} \): \( 2\sqrt{5} \)
  3. Simplified \( \sqrt{12} \): \( 2\sqrt{3} \)