Answer:
1. Option D is correct.
2. Option C is correct
Step-by-step explanation:
1.
Given the statement: four square root of eleven•four square root of ten
"four square root of eleven" translated to [tex]\sqrt[4]{11}[/tex]
"Four square root of ten" translated to [tex]\sqrt[4]{10}[/tex]
then; we have
[tex]\sqrt[4]{11} \cdot \sqrt[4]{10} = \sqrt[4]{11 \cdot 10} =\sqrt[4]{110}[/tex]
Therefore, we get the answer four square root of one hundred ten i.,e [tex]\sqrt[4]{110}[/tex]
2.
To find the simplest form of the expression.
Given: cubed root of twenty four times a to the tenth times b to the sixth.
This translate to: [tex]\sqrt[3]{24 \cdot a^{10} \cdot b^6}[/tex]
Simplify: [tex]\sqrt[3]{24 \cdot a^{10} \cdot b^6}[/tex]
We know:
[tex]\sqrt[n]{a^n} = a[/tex]
[tex](a^n)^m = a^{nm}[/tex]
[tex]a^{n+m} = a^n \cdot a^m[/tex]
then;
[tex]\sqrt[3]{24 \cdot a^{10} \cdot b^6}[/tex]
= [tex]\sqrt[3]{8 \cdot 3 \cdot a^9 \cdot a \cdot (b^2)^3}[/tex]
=[tex]\sqrt[3]{2^3 \cdot 3 \cdot (a^3)^3 \cdot a \cdot (b^2)^3}[/tex]
=[tex]2 \cdot a^3 \cdot b^2\cdot \sqrt[3]{3 \cdot a}[/tex]
or
=[tex]2a^3b^2\sqrt[3]{3a}[/tex]
Therefore, the simplest form of the given expression is, [tex]2a^3b^2\sqrt[3]{3a}[/tex] or [tex]2a^3b^2 \text{cubed root of three times a}[/tex]
