Math Problem Statement

What is the simplified form of the square root of 126 (√126)?

Solution

The image shows the square root of 126, 126\sqrt{126}.

To simplify 126\sqrt{126}:

  1. Factor 126 into its prime factors:
    126=2×32×7126 = 2 \times 3^2 \times 7

  2. Apply the square root to the prime factors:
    126=2×32×7=32×2×7\sqrt{126} = \sqrt{2 \times 3^2 \times 7} = \sqrt{3^2} \times \sqrt{2 \times 7} 126=3×14\sqrt{126} = 3 \times \sqrt{14}

Thus, the simplified form of 126\sqrt{126} is 3143\sqrt{14}.

Would you like further details or explanations on this simplification?

Here are 5 related questions you might find useful:

  1. How do you factor larger numbers into prime factors?
  2. What is the process of simplifying square roots in more complex cases?
  3. How do you rationalize square roots with fractions or decimals?
  4. Can irrational numbers like 14\sqrt{14} be approximated as decimals?
  5. How do square roots apply in real-world problem-solving scenarios?

Tip: Always check for perfect squares within a number when simplifying square roots!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization
Simplifying Expressions

Formulas

√(a * b) = √a * √b

Theorems

Fundamental Theorem of Arithmetic

Suitable Grade Level

Grades 8-10