Answer:
1.
Perimeter of a rectangle is given by:
[tex]P=2(l+b)[/tex]
Given:
Length of a rectangle(l) = [tex]4\sqrt{2}[/tex] unit and a width(w) of a rectangle = [tex]5+\sqrt{6}[/tex] units.
then;
[tex]P= 2(4\sqrt{2}+5+\sqrt{6}) = 8\sqrt{2}+10+2\sqrt{6} = 10+8\sqrt{2}+2\sqrt{6}[/tex] units.
Therefore, the perimeter of a rectangle is [tex] 10+8\sqrt{2}+2\sqrt{6}[/tex] units.
2.
Simplify: [tex]4\sqrt[3]{3}(7+6\sqrt[3]{9)}[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]28\sqrt[3]{7} + 36\sqrt[3]{27}[/tex]
[tex]28\sqrt[3]{7} + 36 \cdot 3 = 28\sqrt[3]{7} + 108[/tex]
Therefore, the simplified given expression is, [tex]28\sqrt[3]{7} + 108[/tex]
3.
Area of a circle(A) is given by:
[tex]A = \pi r^2[/tex] where r is the radius of the circle.
Given: Area of circle = [tex]100 \pi[/tex] square feet
then;
[tex]100 \pi = \pi r^2[/tex]
⇒[tex]100 = r^2[/tex]
Simplify:
[tex]r = \sqrt{100} = 10[/tex] ft.
Therefore, the radius of the circle is 10 ft.
4.
Volume of a cube is given by:
[tex]V = s^3[/tex] where s is the side length of a cube.
Given: Volume of a cube = 1536 cubic inches.
Substitute the given value to find s;
[tex]1536 = s^3[/tex]
Simplify:
[tex]s=\sqrt[3]{1536} inches[/tex]
Therefore, the length of side of a cube is, 11.54 inches.
5.
Solve: [tex]\sqrt[4]{2p+2} = 3[/tex]
then;
[tex]2p+2 = 3^4[/tex]
2p+2 = 81
Subtract 2 from both sides we get;
2p = 79
Divide 2 both sides we get;
p = 39.5
Therefore, the value of p is 39.5.
