Simplify.
$\sqrt{63}$ = $\square \sqrt{\square}$
Answer (2)
Find the prime factorization of 63: 63 = 3 2 × 7 .
Rewrite the square root: 63 = 9 × 7 .
Use the property of square roots to separate the perfect square: 9 × 7 = 9 × 7 .
Simplify: 63 = 3 7 .
Explanation
Understanding the Problem We are asked to simplify the expression 63 . This means we want to find the largest perfect square that divides 63 and then use the property ab = a ⋅ b to simplify the expression.
Prime Factorization First, we find the prime factorization of 63. We have 63 = 9 × 7 = 3 2 × 7 .
Rewriting the Expression We can rewrite 63 as 9 × 7 . Using the property of square roots, we have 9 × 7 = 9 × 7 .
Simplifying the Square Root Since 9 = 3 , we have 63 = 3 7 .
Examples
Square roots are used in many areas of math and science. For example, when calculating the distance between two points in a plane, we use the distance formula, which involves square roots. Also, when dealing with right triangles and the Pythagorean theorem, square roots are often needed to find the length of a side. Simplifying square roots helps in obtaining more manageable and understandable expressions in these calculations.
To simplify 63 , we find the prime factorization as 3 2 × 7 . Rewriting it, we get 63 = 9 × 7 = 9 × 7 , which simplifies to 3 7 . Therefore, the simplified form is 63 = 3 7 .
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