Math Problem Statement

what is the square root of 73

Solution

The square root of 73 is approximately:

738.544\sqrt{73} \approx 8.544

Since 73 is not a perfect square, its square root is an irrational number. It can be left in its exact form as 73\sqrt{73} or approximated as needed.

Would you like a more detailed breakdown of how to estimate square roots?

Related Questions:

  1. What are some methods to estimate square roots without a calculator?
  2. How do you determine if a number is a perfect square?
  3. What is the prime factorization of 73?
  4. How can we express 73\sqrt{73} in terms of continued fractions?
  5. What is the closest perfect square to 73?

Tip:

If you need a quick estimate for a square root, find the two closest perfect squares. Here, 64=8264 = 8^2 and 81=9281 = 9^2, so 73\sqrt{73} is between 8 and 9.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Irrational Numbers
Approximation

Formulas

Square root function √x

Theorems

Properties of irrational numbers
Square root approximation methods

Suitable Grade Level

Grades 7-9