IDNLearn.com is designed to help you find the answers you need quickly and easily. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.
Sagot :
To simplify the square root of 147, we can follow these steps:
1. Prime Factorization:
- Start by performing the prime factorization of 147. Break down 147 into its prime factors.
- 147 is divisible by 3 (since [tex]\( 1 + 4 + 7 = 12 \)[/tex]), so:
[tex]\[ 147 \div 3 = 49 \][/tex]
- Now factor 49. Since 49 is [tex]\( 7 \times 7 \)[/tex], we have:
[tex]\[ 49 = 7^2 \][/tex]
Therefore, the prime factorization of 147 is:
[tex]\[ 147 = 3 \times 7^2 \][/tex]
2. Simplify the Square Root:
- Now apply the square root to the prime factorization:
[tex]\[ \sqrt{147} = \sqrt{3 \times 7^2} \][/tex]
- Since the square root of a product is the product of the square roots, we can separate the terms:
[tex]\[ \sqrt{147} = \sqrt{3} \times \sqrt{7^2} \][/tex]
- Evaluate the square root of [tex]\(7^2\)[/tex]:
[tex]\[ \sqrt{7^2} = 7 \][/tex]
- Combine the simplified terms:
[tex]\[ \sqrt{147} = 7 \times \sqrt{3} \][/tex]
So, the simplest radical form of [tex]\(\sqrt{147}\)[/tex] is:
[tex]\[ 7\sqrt{3} \][/tex]
To provide you with the numerical result:
The approximate value of [tex]\(7\sqrt{3}\)[/tex] is 12.12435565298214 when calculated.
1. Prime Factorization:
- Start by performing the prime factorization of 147. Break down 147 into its prime factors.
- 147 is divisible by 3 (since [tex]\( 1 + 4 + 7 = 12 \)[/tex]), so:
[tex]\[ 147 \div 3 = 49 \][/tex]
- Now factor 49. Since 49 is [tex]\( 7 \times 7 \)[/tex], we have:
[tex]\[ 49 = 7^2 \][/tex]
Therefore, the prime factorization of 147 is:
[tex]\[ 147 = 3 \times 7^2 \][/tex]
2. Simplify the Square Root:
- Now apply the square root to the prime factorization:
[tex]\[ \sqrt{147} = \sqrt{3 \times 7^2} \][/tex]
- Since the square root of a product is the product of the square roots, we can separate the terms:
[tex]\[ \sqrt{147} = \sqrt{3} \times \sqrt{7^2} \][/tex]
- Evaluate the square root of [tex]\(7^2\)[/tex]:
[tex]\[ \sqrt{7^2} = 7 \][/tex]
- Combine the simplified terms:
[tex]\[ \sqrt{147} = 7 \times \sqrt{3} \][/tex]
So, the simplest radical form of [tex]\(\sqrt{147}\)[/tex] is:
[tex]\[ 7\sqrt{3} \][/tex]
To provide you with the numerical result:
The approximate value of [tex]\(7\sqrt{3}\)[/tex] is 12.12435565298214 when calculated.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Accurate answers are just a click away at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.