IDNLearn.com offers a unique blend of expert answers and community insights. Ask your questions and receive reliable and comprehensive answers from our dedicated community of professionals.

Simplify:

[tex]\[
\sqrt{5uw^5} \sqrt{15u^8w}
\][/tex]

Assume all variables represent positive real numbers.


Sagot :

Of course! Let's simplify the expression [tex]\(\sqrt{5 u w^5} \sqrt{15 u^8 w}\)[/tex] step by step, assuming all variables are positive real numbers.

1. Combine the expressions inside the square roots:
[tex]\[ \sqrt{5 u w^5} \sqrt{15 u^8 w} = \sqrt{(5 u w^5) (15 u^8 w)} \][/tex]

2. Multiply the expressions under the square root:
[tex]\[ \sqrt{(5 u w^5) (15 u^8 w)} = \sqrt{5 \cdot 15 \cdot u \cdot u^8 \cdot w^5 \cdot w} \][/tex]

3. Simplify the multiplication inside the square root:
[tex]\[ 5 \cdot 15 = 75 \][/tex]
[tex]\[ u \cdot u^8 = u^9 \][/tex]
[tex]\[ w^5 \cdot w = w^6 \][/tex]
So the expression becomes:
[tex]\[ \sqrt{75 u^9 w^6} \][/tex]

4. Break down the components of the square root:
[tex]\[ 75 u^9 w^6 \][/tex]

5. Simplify each component separately inside the square root:
[tex]\[ \sqrt{75} = \sqrt{25 \cdot 3} = 5 \sqrt{3} \][/tex]
[tex]\[ \sqrt{u^9} = u^{9/2} = u^4 \sqrt{u} \][/tex]
[tex]\[ \sqrt{w^6} = w^{6/2} = w^3 \][/tex]

6. Combine the simplified parts:
[tex]\[ \sqrt{75 u^9 w^6} = 5 \sqrt{3} u^4 \sqrt{u} w^3 \][/tex]

7. Combine like terms:
[tex]\[ 5 \sqrt{3} u^4 \sqrt{u} w^3 = 5 u^4 w^3 \sqrt{3u} \][/tex]

Therefore, the simplified expression is:
[tex]\[ \boxed{5u^4w^3 \sqrt{3u}} \][/tex]
We 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. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.