Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To solve the given problem [tex]\( 4 \sqrt{2} \times 6 \sqrt{18} \)[/tex], follow these steps:
1. Separate Constants and Radicals:
- The given expression is [tex]\( 4 \sqrt{2} \times 6 \sqrt{18} \)[/tex].
- Rewrite this as [tex]\( (4 \times 6) \times (\sqrt{2} \times \sqrt{18}) \)[/tex].
2. Multiply the Constants:
- The constants [tex]\(4\)[/tex] and [tex]\(6\)[/tex] multiply to give [tex]\(4 \times 6 = 24\)[/tex].
3. Multiply the Square Roots:
- The radicals [tex]\( \sqrt{2} \times \sqrt{18} \)[/tex] can be simplified by using the property of square roots: [tex]\( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \)[/tex].
- Therefore, [tex]\( \sqrt{2} \times \sqrt{18} = \sqrt{2 \times 18} = \sqrt{36} \)[/tex].
4. Simplify the Square Root:
- Next, simplify [tex]\( \sqrt{36} \)[/tex]. Since [tex]\(36\)[/tex] is a perfect square, [tex]\( \sqrt{36} = 6 \)[/tex].
5. Final Multiplication:
- Now, multiply the constant [tex]\( 24 \)[/tex] by the simplified square root [tex]\( 6 \)[/tex]:
[tex]\[ 24 \times 6 = 144 \][/tex]
Thus, the complete simplified expression of [tex]\( 4 \sqrt{2} \times 6 \sqrt{18} \)[/tex] is [tex]\( 144 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{144} \][/tex]
1. Separate Constants and Radicals:
- The given expression is [tex]\( 4 \sqrt{2} \times 6 \sqrt{18} \)[/tex].
- Rewrite this as [tex]\( (4 \times 6) \times (\sqrt{2} \times \sqrt{18}) \)[/tex].
2. Multiply the Constants:
- The constants [tex]\(4\)[/tex] and [tex]\(6\)[/tex] multiply to give [tex]\(4 \times 6 = 24\)[/tex].
3. Multiply the Square Roots:
- The radicals [tex]\( \sqrt{2} \times \sqrt{18} \)[/tex] can be simplified by using the property of square roots: [tex]\( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \)[/tex].
- Therefore, [tex]\( \sqrt{2} \times \sqrt{18} = \sqrt{2 \times 18} = \sqrt{36} \)[/tex].
4. Simplify the Square Root:
- Next, simplify [tex]\( \sqrt{36} \)[/tex]. Since [tex]\(36\)[/tex] is a perfect square, [tex]\( \sqrt{36} = 6 \)[/tex].
5. Final Multiplication:
- Now, multiply the constant [tex]\( 24 \)[/tex] by the simplified square root [tex]\( 6 \)[/tex]:
[tex]\[ 24 \times 6 = 144 \][/tex]
Thus, the complete simplified expression of [tex]\( 4 \sqrt{2} \times 6 \sqrt{18} \)[/tex] is [tex]\( 144 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{144} \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.