Question

3 questions! Simplify the following and leave them in radical notation. Show your work.

Answer 1

all work is pictured and shown

Answer 2

Explanation:

a)

First, when simplifying radicals, we prime factorize the number within the radical. In this case, it's
`2^(5)`. For square roots, when we have 2 of the same prime number, it goes outside the radical. However, when it goes outside the radical, we only write that number once.

`√(32) \\=√(2*2*2*2*2) \\=2*2√(2) \\=4√(2)`

b)

`\sqrt{125x^(2)y^(7)  } \\=√(5*5*5*x*x*y*y*y*y*y*y*y)\\=5*x*y*y*y√(5y)\\=5xy^(3)√(5y)`

c)

For this, we want the cubic root, so we need at least 3 of a number for it to go outside the radical.

`\sqrt[3]{24x^(3)y^(8)  } \\=\sqrt[3]{2*2*2*3*x*x*x*y*y*y*y*y*y*y*y} \\=2*x*y*y\sqrt[3]{3*y*y} \\=2xy^(2) \sqrt[3]{3y^(2) }`