Get the answers you've been searching for with IDNLearn.com. Explore a wide array of topics and find reliable answers from our experienced community members.
Sagot :
To simplify the expression [tex]\(\sqrt{50} + \sqrt{2}\)[/tex], let's follow a step-by-step process.
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- We start by breaking down [tex]\(50\)[/tex] into its prime factors: [tex]\(50 = 25 \times 2\)[/tex].
- Therefore, [tex]\(\sqrt{50} = \sqrt{25 \times 2}\)[/tex].
- Recognizing that [tex]\(\sqrt{25}\)[/tex] is a perfect square, we have [tex]\(\sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \times \sqrt{2}\)[/tex].
Consequently, [tex]\(\sqrt{50}\)[/tex] simplifies to [tex]\(5\sqrt{2}\)[/tex].
2. Simplify [tex]\(\sqrt{2}\)[/tex]:
- [tex]\(\sqrt{2}\)[/tex] is already in its simplest form as it cannot be simplified further.
3. Combine the simplified terms:
- Now we combine the terms we obtained: [tex]\(5\sqrt{2}\)[/tex] and [tex]\(\sqrt{2}\)[/tex].
- Since both terms include [tex]\(\sqrt{2}\)[/tex], we can add them directly: [tex]\(5\sqrt{2} + \sqrt{2} = (5 + 1)\sqrt{2} = 6\sqrt{2}\)[/tex].
So, the simplified form of the original expression [tex]\(\sqrt{50} + \sqrt{2}\)[/tex] is [tex]\(6\sqrt{2}\)[/tex].
However, if we were to express the numerical or decimal value of the sum:
- [tex]\(\sqrt{50} \approx 7.0710678118654755\)[/tex]
- [tex]\(\sqrt{2} \approx 1.4142135623730951\)[/tex]
- Summing these, we get [tex]\(7.0710678118654755 + 1.4142135623730951 \approx 8.485281374238571\)[/tex]
So the decimal approximation of [tex]\(\sqrt{50} + \sqrt{2}\)[/tex] is approximately [tex]\(8.485281374238571\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- We start by breaking down [tex]\(50\)[/tex] into its prime factors: [tex]\(50 = 25 \times 2\)[/tex].
- Therefore, [tex]\(\sqrt{50} = \sqrt{25 \times 2}\)[/tex].
- Recognizing that [tex]\(\sqrt{25}\)[/tex] is a perfect square, we have [tex]\(\sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \times \sqrt{2}\)[/tex].
Consequently, [tex]\(\sqrt{50}\)[/tex] simplifies to [tex]\(5\sqrt{2}\)[/tex].
2. Simplify [tex]\(\sqrt{2}\)[/tex]:
- [tex]\(\sqrt{2}\)[/tex] is already in its simplest form as it cannot be simplified further.
3. Combine the simplified terms:
- Now we combine the terms we obtained: [tex]\(5\sqrt{2}\)[/tex] and [tex]\(\sqrt{2}\)[/tex].
- Since both terms include [tex]\(\sqrt{2}\)[/tex], we can add them directly: [tex]\(5\sqrt{2} + \sqrt{2} = (5 + 1)\sqrt{2} = 6\sqrt{2}\)[/tex].
So, the simplified form of the original expression [tex]\(\sqrt{50} + \sqrt{2}\)[/tex] is [tex]\(6\sqrt{2}\)[/tex].
However, if we were to express the numerical or decimal value of the sum:
- [tex]\(\sqrt{50} \approx 7.0710678118654755\)[/tex]
- [tex]\(\sqrt{2} \approx 1.4142135623730951\)[/tex]
- Summing these, we get [tex]\(7.0710678118654755 + 1.4142135623730951 \approx 8.485281374238571\)[/tex]
So the decimal approximation of [tex]\(\sqrt{50} + \sqrt{2}\)[/tex] is approximately [tex]\(8.485281374238571\)[/tex].
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.