What is the simplified form of square root of 48 n 9?
√(48n^9)
= √16 *√3*√n^8 *√n
= 4n^4 √(3n)
Oh, sqrt(48n9)? Well, let me put on my math clown hat for a second. *dons hat* Okay, let's simplify this. First, let's break down the expression. The square root of 48 can be simplified as the square root of 16 times 3. And we can also take the square root of 9. So, now we have the square root of 16 which is 4, times the square root of 3, times the square root of 9 which is 3. Putting it all together, the simplified form of sqrt(48n9) is 4 x 3 x sqrt(3), or simply 12 sqrt(3). Voila!
To simplify the expression, we need to break down the square root of 48 and the square root of 9 separately:
1. Begin with the square root of 48:
- Note that 48 can be factored into 16 * 3.
- The square root of 16 is 4.
- Therefore, the square root of 48 can be written as 4 * √3.
2. Now, consider the square root of 9:
- The square root of 9 is simply 3.
Combining the two simplified forms, we get:
4 * √3 * 3.
Hence, the simplified form of the expression is 12√3.
To simplify the expression √48n^9, we can break it down into factors and then simplify each factor separately.
First, let's simplify the square root of 48. Notice that 48 can be factored into 16 * 3. Taking the square root of each factor, we have:
√48 = √(16 * 3) = √16 * √3 = 4√3
Next, let's simplify the square root of n^9. Since the exponent is an odd number, we can split the exponent into an even and an odd part:
n^9 = n^(8+1) = n^8 * n^1
Now, we can simplify the square root of n^8 and n^1 separately:
√n^8 = √(n^4)^2 = n^4
√n^1 = √n = n
Combining these simplified factors, we have:
√48n^9 = 4√3n^4