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
3 square root 32
2 square root 18
5 square root 48
3 square root 54
Thanks :)
Hi! Just to clarify, are those numbers on the left (the 2, 3, 6, 3, etc.) are multiplied with the squareroot terms or are written as small number which is therefore part of the radical sign?
They are multiplied
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
Sure! I can help you simplify these mixed radicals and show you how it's done.
To simplify a square root with a whole number in front of it, you need to find the largest perfect square that can be taken out from the number under the radical.
Let's simplify each of the mixed radicals you provided:
1) 2√48:
To start, we can factor 48 into its prime factors: 48 = 2 * 2 * 2 * 2 * 3. Notice that 2 * 2 = 4 is a perfect square. We can take it outside of the radical: 2 * √(4 * 3) = 2 * 2 * √3 = 4√3.
2) 3√81:
Since 81 is already a perfect square (9 * 9 = 81), we can take out the square root: 3 * √(9 * 9) = 3 * 9 = 27.
3) 6√12:
We can factor 12 into its prime factors: 12 = 2 * 2 * 3. Again, 2 * 2 = 4 is a perfect square. Taking it outside of the radical gives us: 2 * √(4 * 3) = 2 * 2 * √3 = 4√3.
4) 3√32:
Similarly, we can factor 32 into its prime factors: 32 = 2 * 2 * 2 * 2 * 2. Taking out the largest perfect square (2 * 2 = 4) gives us: 2 * √(4 * 2) = 2 * 2 * √2 = 4√2.
5) 2√18:
Factoring 18 gives us 2 * 3 * 3. Taking the largest perfect square (3 * 3 = 9) leaves us with: 3 * √(2 * 9) = 3 * 3 * √2 = 9√2.
6) 5√48:
Factorizing 48 gives us 2 * 2 * 2 * 2 * 3. The largest perfect square is 4 * 4 = 16. Taking it outside the radical yields: 4 * √(3 * 16) = 4 * 4 * √3 = 16√3.
7) 3√54:
Factor 54 to get 2 * 3 * 3 * 3. Taking the largest perfect square (3 * 3 = 9) out, we get: 3 * √(3 * 9) = 3 * 3 * √3 = 9√3.
So, the simplified forms of the mixed radicals are:
1) 2√48 = 4√3
2) 3√81 = 27
3) 6√12 = 4√3
4) 3√32 = 4√2
5) 2√18 = 9√2
6) 5√48 = 16√3
7) 3√54 = 9√3
I hope this helps you understand how to simplify mixed radicals!