Question

4√5√√48+3√40√√12-2√15√√27

Answer 1

4√5√√48+3√40√√12-2√15√√27 =41.1996333894

                           

Answer 2

To simplify the expression, let's start by simplifying each of the terms step-by-step.

1. √48 The square root of 48 can be simplified by breaking it down into its prime factors: 48 = 2^4 * 3 √48 = √(2^4 * 3) = √(2^4) * √3 = 2^2 * √3 = 4√3

2. √12 Similarly, the square root of 12 can be simplified: 12 = 2^2 * 3 √12 = √(2^2 * 3) = √(2^2) * √3 = 2 * √3

3. √27 The square root of 27 can be simplified as well: 27 = 3^3 √27 = √(3^3) = √(3^2) * √3 = 3 * √3

Now let's put everything together:

4√(5√(√48)) + 3√(40√(√12)) - 2√(15√(√27))

4√(5√(4√3)) + 3√(40√(2√3)) - 2√(15√(3))

Now, let's continue simplifying:

1. 4√(5√(4√3)) Since 4√3 = 4 * √3 = 2 * (2√3), we get: 4√(5√(4√3)) = 4√(5 * 2 * (2√3)) = 4√(10 * (2√3)) = 4√(20√3)

2. 3√(40√(2√3)) Since 3√(2√3) = 3 * √(2√3) = 3 * (2√3) = 6√3, we get: 3√(40√(2√3)) = 3√(40 * 6√3) = 3√(240√3)

3. 2√(15√3) This term is already simplified, so we leave it as is.

Now the expression becomes:

4√(20√3) + 3√(240√3) - 2√(15√3)

Next, we can combine like terms:

4√(20√3) = 4 * √(20√3) = 4 * (2√5) = 8√5

3√(240√3) = 3 * √(240√3) = 3 * (4√15) = 12√15

Now the expression becomes:

8√5 + 12√15 - 2√(15√3)

The term 2√(15√3) cannot be simplified any further since it doesn't have any common factors with the other terms. So the final simplified expression is:

8√5 + 12√15 - 2√(15√3)