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

Question

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 :)

Answer 1

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

Answer 2

the square root of 20 minus the sqare root of 5 plus the square root of 45

Answer 3

Divide 8 to the square root of 6/2