Simplify square root of 63
The Correct answer and Explanation is :
The correct answer is: {3\sqrt{7}}
The simplified form of the square root of 63 is:
[
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}
]
Explanation
- Factorization of 63:
To simplify a square root, first break down the number into its prime factors. For 63, the prime factorization is:
[
63 = 9 \times 7
]
We split 63 into the product of 9 and 7 because 9 is a perfect square. - Taking the square root of perfect squares:
We can take the square root of any perfect square easily. Since 9 is a perfect square, its square root is:
[
\sqrt{9} = 3
] - Simplifying the expression:
Using the property of square roots, we can split the original square root as:
[
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7}
]
Now, substitute the value of (\sqrt{9}):
[
\sqrt{63} = 3 \times \sqrt{7}
] - Final simplified form:
Since (\sqrt{7}) is not a perfect square and cannot be simplified further, the final simplified form of (\sqrt{63}) is:
[
\boxed{3\sqrt{7}}
]
Why Simplify Square Roots?
Simplifying square roots is important because it expresses the root in a more manageable form, making it easier to work with in equations or other math problems. In real-life applications, such as engineering, physics, or construction, this simplification helps in making calculations faster and clearer.
This process follows the rule of identifying and pulling out perfect squares, leaving the non-perfect square factors under the square root.