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:

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