Simplify 3 square root of 20 / square root of 5

Let's simplify \sqrt{75}

75

​  square root of, 75, end square root by removing all perfect squares from inside the square root.

We start by factoring 757575, looking for a perfect square:

75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5

2

×375, equals, 5, times, 5, times, 3, equals, start color blueD, 5, start superscript, 2, end superscript, end color blueD, times, 3.

We found one! This allows us to simplify the radical:

\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} &=5\cdot \sqrt{3} \end{aligned}

75

​  

​  

=

5

2

⋅3

​  

=

5

2

​  ⋅

3

​  

=5⋅

3

​  

​  

So \sqrt{75}=5\sqrt{3}

75

​  =5

3

​  square root of, 75, end square root, equals, 5, square root of, 3, end square root.Let's simplify \sqrt{75}

75

​  square root of, 75, end square root by removing all perfect squares from inside the square root.

We start by factoring 757575, looking for a perfect square:

75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5

2

×375, equals, 5, times, 5, times, 3, equals, start color blueD, 5, start superscript, 2, end superscript, end color blueD, times, 3.

We found one! This allows us to simplify the radical:

\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} &=5\cdot \sqrt{3} \end{aligned}

75

​  

​  

=

5

2

⋅3

​  

=

5

2

​  ⋅

3

​  

=5⋅

3

​  

​  

So \sqrt{75}=5\sqrt{3}

75

​  =5

3

​  square root of, 75, end square root, equals, 5, square root of, 3, end square root.

you need to add a picture

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c