Multiply √11 ⋅6√7 . Give an exact answer.(1 point)
√11 ⋅6√7 can be simplified by multiplying the coefficients and combining the radicals:
√11 ⋅6√7 = 6√(11) ⋅ √(7) = 6√(11⋅7) = 6√(77)
So, the exact answer is 6√77.
To multiply the square root of 11 (√11) by 6 times the square root of 7 (6√7), we can use the property of square roots which states that the square root of a product is equal to the product of the square roots.
So, √11 ⋅ 6√7 = √(11) × 6√(7).
Next, we can simplify the expression by multiplying the numbers outside the square roots and then multiplying the numbers inside the square roots.
6√(7) can be written as 6 × √(7) = √(36) × √(7) = √(36 × 7) = √(252).
Therefore, √11 ⋅ 6√7 = √(11) × √(252).
Now, using the property of square roots again, we can combine the two square roots into a single square root:
√(11 × 252) = √(2772).
Thus, the exact answer is √(2772).
To multiply √11 and 6√7, you can follow these steps:
Step 1: Simplify both square roots if possible.
- √11 is already simplified because 11 cannot be further simplified.
- 6√7 can be simplified by multiplying the coefficient (6) with the coefficient inside the square root (7), resulting in 42√7.
Step 2: Multiply the coefficients and multiply the square roots.
- Multiply the coefficients: 1 (from √11) and 42 (from 6√7), resulting in 42.
- Multiply the square roots: √11 (from √11) and √7 (from 6√7), resulting in √(11*7) = √77.
Step 3: Combine the results.
- The result of step 2 is 42√77.
So, √11 ⋅ 6√7 = 42√77.