Math Problem Statement

b^2 = \dfrac{16}{121}

Solution

To solve the equation b2=16121b^2 = \dfrac{16}{121}, follow these steps:

  1. Take the square root of both sides: To solve for bb, take the square root of both sides of the equation.

    b=±16121b = \pm \sqrt{\dfrac{16}{121}}
  2. Simplify the square root:

    b=±16121b = \pm \dfrac{\sqrt{16}}{\sqrt{121}} b=±411b = \pm \dfrac{4}{11}

So, the solution is:

b=411orb=411b = \dfrac{4}{11} \quad \text{or} \quad b = -\dfrac{4}{11}

Would you like any further details or have any questions?

Here are some related questions you might find interesting:

  1. How do you solve equations involving square roots?
  2. What happens if the square root does not result in a rational number?
  3. Can you explain the concept of rational and irrational numbers?
  4. How does squaring both sides of an equation affect the solution set?
  5. What is the geometric interpretation of b2=16121b^2 = \dfrac{16}{121}?

Tip: When dealing with square roots, always consider both the positive and negative roots unless the problem specifically states otherwise.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots
Rational Numbers

Formulas

Square root formula: \(\sqrt{a} = b\) where \(b^2 = a\)

Theorems

Properties of square roots
Square root of a quotient property: \(\sqrt{\dfrac{a}{b}} = \dfrac{\sqrt{a}}{\sqrt{b}}\)

Suitable Grade Level

Grades 7-9