\sf \sqrt{29}
\sf \sqrt{31}
\sf \sqrt{33}
\sf \sqrt{35}

The numbers you listed are square roots of different values:

1. \(\sqrt{29}\)
2. \(\sqrt{31}\)
3. \(\sqrt{33}\)
4. \(\sqrt{35}\)

These square roots are all irrational numbers, meaning they cannot be expressed as a simple fraction, and their decimal representations go on forever without repeating. Below are the approximate decimal values:

1. \(\sqrt{29} \approx 5.3852\)
2. \(\sqrt{31} \approx 5.5680\)
3. \(\sqrt{33} \approx 5.7446\)
4. \(\sqrt{35} \approx 5.9161\)

Each of these square roots is a little larger than the square root of the previous number.

Would you like to explore more details or have any other questions? Here are some related questions:

1. How do you determine whether a square root is rational or irrational?
2. What is the process for estimating the value of a square root without a calculator?
3. How can square roots be simplified if they involve perfect squares?
4. What are some common uses of square roots in geometry and algebra?
5. How do square roots relate to the Pythagorean Theorem?

**Tip:** Remember that if the number under the square root (the radicand) is not a perfect square, the square root will be an irrational number.

Explore the square roots of 29, 31, 33, and 35 with their approximate decimal values and properties. Learn about irrational numbers and their significance in mathematics. Suitable for advanced high school students.

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