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.