simplifying radicals: sqrt 50, sqrt 80*n^2

[honorspianist]

Hi there! Great site.

Could you please help me simplify these radicals:

1. Simplify to simplest radical form: sqrt 50

2. Simplify sqrt 80*n^2

Thank you!

 

[stapel]

Factor the argument of the radical. Whatever you've got two of (if anything), take out. Whatever is left over (if anything), leave inside. For instance:

. . . . .sqrt[4] = sqrt[2×2] = 2

. . . . .sqrt[8] = sqrt[2×2×2] = 2sqrt[2]

. . . . .sqrt[75x²] = sqrt[3×5×5×(x)×(x)] = 5xsqrt[3]

. . . . .sqrt[9y³] = sqrt[3×3×y×y×y] = 2ysqrt[y]

Follow this procedure with your exercises.

Eliz.

 

[swelkey]

To clarify

It may not be quite clear what Stapel was doing in the above. It's called prime factorization. Any integer is either prime, or can be split up into some primes multiplied together. Here are some examples:
\(\displaystyle 25 = 5 \times 5\)
\(\displaystyle 12 = 2 \times 2 \times 3\)
\(\displaystyle 33 = 3 \times 11\)
Believe it or not, any integer can be split up like this, and you'll always get the same prime numbers. If you do it wrong, you'll still have something left over that isn't prime, and you just split that up too.

Next, yo do the same thing with your variables, like y and x in stapel's examples. As stapel said, anything that's repeated (number or variable) is squared, so you can "un-square" it by making it single and taking it out of the radical. IE
\(\displaystyle \sqrt{90} = \sqrt{2 \times 3 \times 3 \times 5} = 3 \times \sqrt{2 \times 5}\)