Math Problem Statement

Calculate the following square roots and cube roots. Round your answers to three decimal places.

Part A:
11 1/2

Solution

To solve Part A, we need to calculate the square root of 11, denoted as 111/211^{1/2}.

Calculation:

The square root of a number xx is written as x1/2x^{1/2}:

111/2=1111^{1/2} = \sqrt{11}

Using a calculator, we find:

113.317\sqrt{11} \approx 3.317

Final Answer:

111/23.31711^{1/2} \approx 3.317

Would you like further details or have any questions?

Here are 5 related questions to explore:

  1. How do you calculate the cube root of 11?
  2. What is the square root of 15, rounded to three decimal places?
  3. How would you find the fourth root of a number like 16?
  4. What is the difference between square roots and cube roots?
  5. How do you simplify expressions involving roots like 25+4\sqrt{25} + \sqrt{4}?

Tip: When calculating square or cube roots, try to memorize the roots of smaller numbers like 1 through 10 for quicker estimations.

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Math Problem Analysis

Mathematical Concepts

Roots
Square Roots
Radicals

Formulas

x^(1/2) = sqrt(x)

Theorems

Radical simplification theorem

Suitable Grade Level

Grades 6-8