Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To simplify the square root of \( \sqrt{484} \), we will follow the steps you outlined. Here's a detailed step-by-step solution:
1. Write the prime factorization of the radicand:
We start with the number 484 and find its prime factors. The prime factorization of 484 is:
[tex]\[ 484 = 2 \times 2 \times 11 \times 11 \][/tex]
Therefore:
[tex]\[ \sqrt{484} = \sqrt{2 \times 2 \times 11 \times 11} \][/tex]
2. Apply the product property of square roots:
The product property of square roots allows us to split the square root of a product into the product of square roots. Using this property, we can rewrite the radicand as a product of squares:
[tex]\[ \sqrt{2 \times 2 \times 11 \times 11} = \sqrt{2^2} \times \sqrt{11^2} \][/tex]
3. Simplify:
Now, we simplify the square roots of the perfect squares:
[tex]\[ \sqrt{2^2} = 2 \][/tex]
[tex]\[ \sqrt{11^2} = 11 \][/tex]
Therefore:
[tex]\[ \sqrt{2^2} \times \sqrt{11^2} = 2 \times 11 = 22 \][/tex]
Putting it all together, we have:
[tex]\[ \sqrt{484} = 22 \][/tex]
Thus, the simplified form of [tex]\( \sqrt{484} \)[/tex] is [tex]\( 22 \)[/tex].
1. Write the prime factorization of the radicand:
We start with the number 484 and find its prime factors. The prime factorization of 484 is:
[tex]\[ 484 = 2 \times 2 \times 11 \times 11 \][/tex]
Therefore:
[tex]\[ \sqrt{484} = \sqrt{2 \times 2 \times 11 \times 11} \][/tex]
2. Apply the product property of square roots:
The product property of square roots allows us to split the square root of a product into the product of square roots. Using this property, we can rewrite the radicand as a product of squares:
[tex]\[ \sqrt{2 \times 2 \times 11 \times 11} = \sqrt{2^2} \times \sqrt{11^2} \][/tex]
3. Simplify:
Now, we simplify the square roots of the perfect squares:
[tex]\[ \sqrt{2^2} = 2 \][/tex]
[tex]\[ \sqrt{11^2} = 11 \][/tex]
Therefore:
[tex]\[ \sqrt{2^2} \times \sqrt{11^2} = 2 \times 11 = 22 \][/tex]
Putting it all together, we have:
[tex]\[ \sqrt{484} = 22 \][/tex]
Thus, the simplified form of [tex]\( \sqrt{484} \)[/tex] is [tex]\( 22 \)[/tex].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.