Math simplifying mixed radicals
posted by Miley
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 :)

Jai
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 
john
the square root of 20 minus the sqare root of 5 plus the square root of 45
Respond to this Question
Similar Questions

Math(radicals or square roots)
i need a explanation for this equation: 5 radical(square root) 108 over 25 the 5 is in front of the square rooted number and it is a fraction PlEASE HELP :( That is not an equation. It is a number. It sounds like you are describing … 
Math
I need help simplifying radicals. The problem in priticular is the square root of 60x^2 √60x^2 can be simplified this way: √(4 * 15 * x^2) Can you see what to take out from under the square root sign? 
Math
What is the square root of 12? 3.464 Well, that's true, but you could simplify it in radicals. The square root of 12 is the same as saying the square root of 3 times the square root of 4. The square root of 4 is plus or minus 2, so 
simplifying radicals
helo! i know how to simplify radicals but.. I don't get this one. behind of the radical (square root sign) there is a big gap before the number. Many people are saying it's a typo, but.. i don't know. there are a couple like that. … 
Algebra 2
could you walk me thorugh these problems simplfy square root 18  3 times sqaure root of 50 plus 5 times the square root of 80  2 times the square root of 125 I'm having troubles with the square root of 80 all of the other radicals … 
Algebra 1B
I really need help with this but I'm not sure if I'm going to put it in the correct form. The problem says to multiply and simplify by factoring. Assume that all expressions under radicals represents nonnegative numbers. Simplify your … 
Math
Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers. The square root of 243x^6/y^20 to the fifth root. Here is what I have so far: the square root of … 
Calculus
State whether the following are true or false. The square roots of 36 are + and  6. I wrote down false for this cause I thought it was only + 6, but the real answer is true, and I want to know that how can it be negative? 
Math
how do you write radicals as powers? please help me with the following question, I know the answer but I don't know HOW to get it. I must learn this so please help me. y5/3 is under the square root sign sorry I retyped this, but I 
Math simplifying mixed radicals
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: 2 square root 48 3 square root 81 6 square root 12 …