Math Problem Statement

Simplify the square root of 63.

Solution

The expression in the image is 63\sqrt{63}.

To simplify 63\sqrt{63}, we break it down into prime factors:

63=9×7=32×763 = 9 \times 7 = 3^2 \times 7

So, 63\sqrt{63} can be rewritten as:

63=32×7=37\sqrt{63} = \sqrt{3^2 \times 7} = 3\sqrt{7}

Thus, the simplified form of 63\sqrt{63} is 373\sqrt{7}.

Would you like more details or have any further questions? Here are some related questions you might find helpful:

  1. How do you simplify square roots involving larger numbers?
  2. What are the steps for finding the prime factorization of a number?
  3. How would you approximate 7\sqrt{7} to a decimal?
  4. How does simplifying square roots help in solving equations?
  5. Can all square roots be simplified in a similar manner?

Tip: Always check if a number under the square root has a perfect square factor. This helps in simplifying the expression.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization

Formulas

\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)

Theorems

Simplification of Square Roots

Suitable Grade Level

Grades 6-8