Posted by **Miley** on Saturday, September 14, 2013 at 9:00pm.

Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn :

I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are supposed to be multiplied.

2 square root 48

3 square root 81

6 square root 12

3 square root 32

2 square root 18

5 square root 48

3 square root 54

Thanks :)

- Math simplifying mixed radicals -
**Jai**, Saturday, September 14, 2013 at 9:06pm
To do this, you have to factor the radicand (or the number inside the radical sign) and look for perfect squares. For instance,

2 * √(48)

2 * √(16*3)

2 * √(4*4*3)

Express the repeating factors using exponents, so it's easier to see. Since four is multiplied by itself twice,

2 * √((4^2) * 3)

The 4^2 is a perfect square, it's squareroot is equal to 4. Therefore you have,

2 * 4 √(3)

= 8 * √(3)

#2.

3 * √(81)

3 * √(9*9)

3 * √(9^2)

3 * 9

= 27

#3.

6 * √(12)

6 * √(2*2*3)

6 * √((2^2) * 3)

6 * 2 * √(3)

= 12 * √(3)

#4.

3 * √(32)

3 * √(8*4)

3 * √(2*4*4)

3 * √((4^2) * 2)

3 * 4 * √(2)

= 12 * √(2)

Now, try solving the rest.

Hope this helps~ :3

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