3√ 12 x 2√ 5
6√ 80
2√ 15
12√ 15
6√ 15
To simplify each of these expressions, we need to simplify the square roots individually and then multiply or divide accordingly.
1. 3√12 x 2√5:
√12 = √(4 x 3) = 2√3
√5 remains the same
So, 3√12 x 2√5 = 3(2√3)(2√5) = 12√15
2. 6√80:
√80 = √(16 x 5) = 4√5
So, 6√80 = 6(4√5) = 24√5
3. 2√15:
The square root of 15 cannot be simplified any further.
So, 2√15 is already simplified.
4. 12√15:
The square root of 15 cannot be simplified any further.
So, 12√15 is already simplified.
5. 6√15:
The square root of 15 cannot be simplified any further.
So, 6√15 is already simplified.
Simplify 3√ 12 x 2√ 5
6√ 80
2√ 15
12√ 15
6√ 15
To simplify each of these expressions, we can combine like terms and simplify the square roots if possible.
1. 3√12 x 2√5:
√12 = √(4 x 3) = 2√3
√5 remains the same
Thus, 3√12 x 2√5 = 3(2√3)(2√5) = 12√15
2. 6√80:
√80 = √(16 x 5) = 4√5
Therefore, 6√80 = 6(4√5) = 24√5
3. 2√15:
The square root of 15 is the simplest form in this case, so 2√15 cannot be simplified further.
4. 12√15:
The square root of 15 is already simplified, so 12√15 is the simplest form.
5. 6√15:
The square root of 15 is already in its simplest form, so 6√15 is the simplest form.
3√12 x 2√ 5
To simplify 3√12 x 2√5, we can simply multiply the numbers outside the square roots and multiply the numbers inside the square roots:
3√12 x 2√5 = 3 x 2 √(12 x 5) = 6√60
To simplify further, we can find the largest perfect square that divides into 60. Since 60 is divisible by 4, we can write 60 as 4 x 15:
6√60 = 6√(4 x 15)
Now, we can simplify the square root of 4:
6√(4 x 15) = 6 x 2√15 = 12√15
Therefore, 3√12 x 2√5 simplifies to 12√15.
√ 2(4√8-3√10)
To simplify √2(4√8 - 3√10), we can distribute the square root over each term inside the parentheses:
√2(4√8 - 3√10) = √2(4√8) - √2(3√10)
Now, simplify each term:
√2(4√8) = 4√(2 * 8) = 4√16 = 4 * 4 = 16
√2(3√10) = 3√(2 * 10) = 3√20
Thus, the simplified form is:
√2(4√8 - 3√10) = 16 - 3√20
Therefore, the simplified expression is 16 - 3√20.
^3√ 3 x ^3√ 16
To simplify ^3√3 x ^3√16, we can combine the cube roots and multiply the numbers under the radical:
^3√3 x ^3√16 = ^3√(3 x 16) = ^3√48
Now, let's simplify the cube root of 48. We can calculate the prime factorization of 48, which is 2^4 x 3.
^3√48 = ^3√(2^4 x 3) = ^3√(2^3 x 2 x 3) = ^3√(8 x 2 x 3)
Since ^3√8 = 2, we can simplify further:
^3√48 = 2 x ^3√(2 x 3)
= 2 x ^3√6
Therefore, the simplified expression is 2 x ^3√6.