Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To find the cube root of 32, we need to determine the number that, when multiplied by itself three times (or cubed), equals 32. Here is the step-by-step process:
1. Understand the cube root notation: The expression [tex]\(\sqrt[3]{32}\)[/tex] represents the cube root of 32, which is the number [tex]\(x\)[/tex] such that [tex]\(x^3 = 32\)[/tex].
2. Estimate an initial value: We recognize that [tex]\(2^3 = 8\)[/tex] and [tex]\(3^3 = 27\)[/tex]. Since [tex]\(8 < 32 < 27\)[/tex], the cube root of 32 should be between 2 and 3.
3. Narrow down the range: Let's refine our estimate by considering more precise values. We know that [tex]\(2.5^3 = 15.625\)[/tex] and [tex]\(3^3 = 27\)[/tex], and since [tex]\(15.625 < 32 < 27\)[/tex], the cube root of 32 is between 2.5 and 3.
4. Use a more precise approximation: We can refine our guess again. Trying 3.2, we see that:
[tex]\[ 3.2^3 = 3.2 \times 3.2 \times 3.2 = 10.24 \times 3.2 = 32.768 \][/tex]
Since [tex]\(32.768\)[/tex] is close to [tex]\(32\)[/tex], we know the cube root is just slightly less than 3.2.
5. Converge to the exact value: To get even closer, additional computations or tools for more accurate values can be used, but after sufficient refinement:
[tex]\[ \sqrt[3]{32} \approx 3.1748021039363987 \][/tex]
Therefore, the cube root of 32 is approximately [tex]\(3.1748021039363987\)[/tex].
1. Understand the cube root notation: The expression [tex]\(\sqrt[3]{32}\)[/tex] represents the cube root of 32, which is the number [tex]\(x\)[/tex] such that [tex]\(x^3 = 32\)[/tex].
2. Estimate an initial value: We recognize that [tex]\(2^3 = 8\)[/tex] and [tex]\(3^3 = 27\)[/tex]. Since [tex]\(8 < 32 < 27\)[/tex], the cube root of 32 should be between 2 and 3.
3. Narrow down the range: Let's refine our estimate by considering more precise values. We know that [tex]\(2.5^3 = 15.625\)[/tex] and [tex]\(3^3 = 27\)[/tex], and since [tex]\(15.625 < 32 < 27\)[/tex], the cube root of 32 is between 2.5 and 3.
4. Use a more precise approximation: We can refine our guess again. Trying 3.2, we see that:
[tex]\[ 3.2^3 = 3.2 \times 3.2 \times 3.2 = 10.24 \times 3.2 = 32.768 \][/tex]
Since [tex]\(32.768\)[/tex] is close to [tex]\(32\)[/tex], we know the cube root is just slightly less than 3.2.
5. Converge to the exact value: To get even closer, additional computations or tools for more accurate values can be used, but after sufficient refinement:
[tex]\[ \sqrt[3]{32} \approx 3.1748021039363987 \][/tex]
Therefore, the cube root of 32 is approximately [tex]\(3.1748021039363987\)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.