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QUESTION IMAGE

approximate the value of the following square roots, and drag them to t…

Question

approximate the value of the following square roots, and drag them to their corresponding place between two numbers.
drag & drop the answer
√21
√67
√35
√8
note: use ctrl+d to drag the option via keyboard
4 < < 5
2 < < 3
8 < < 9
5 < < 6

Explanation:

Step1: Analyze \( \sqrt{21} \)

Find perfect squares around 21. \( 4^2 = 16 \), \( 5^2 = 25 \). Since \( 16 < 21 < 25 \), \( 4 < \sqrt{21} < 5 \).

Step2: Analyze \( \sqrt{67} \)

Perfect squares: \( 8^2 = 64 \), \( 9^2 = 81 \). \( 64 < 67 < 81 \), so \( 8 < \sqrt{67} < 9 \).

Step3: Analyze \( \sqrt{35} \)

Perfect squares: \( 5^2 = 25 \), \( 6^2 = 36 \). \( 25 < 35 < 36 \), so \( 5 < \sqrt{35} < 6 \).

Step4: Analyze \( \sqrt{8} \)

Perfect squares: \( 2^2 = 4 \), \( 3^2 = 9 \). \( 4 < 8 < 9 \), so \( 2 < \sqrt{8} < 3 \).

Answer:

  • \( 4 < \boldsymbol{\sqrt{21}} < 5 \)
  • \( 2 < \boldsymbol{\sqrt{8}} < 3 \)
  • \( 8 < \boldsymbol{\sqrt{67}} < 9 \)
  • \( 5 < \boldsymbol{\sqrt{35}} < 6 \)