Divide 8√6 / 2 . Provide an exact answer.
To divide 8√6 by 2, we can first simplify the expression by dividing the numbers outside the square root separately, then simplify the square root part.
8 / 2 = 4
√6 is not divisible by 2, so we leave it as it is.
Thus, the simplified expression is 4√6.
To divide 4√10 by √2, we can multiply the numerator and denominator by √2 to rationalize the denominator and simplify the expression.
(4√10 * √2) / (√2 * √2)
Simplifying within each part of the expression:
4 * 2 = 8
√10 * √2 = √(10 * 2) = √20 = 2√5
So the expression becomes:
8√5 / 2
Simplifying further:
8 / 2 = 4
Therefore, the exact answer is 4√5.
To simplify √300, we can break down 300 into its prime factors.
300 = 2 * 2 * 3 * 5 * 5
Now, let's simplify the square root by grouping pairs of the same prime factors:
√(2 * 2 * 3 * 5 * 5)
= √(2^2 * 3 * 5^2)
= 2 * 5 * √3
= 10√3
Therefore, √300 simplifies to 10√3.
To simplify 13√27, we can break down 27 into its prime factors.
27 = 3 * 3 * 3
Now, let's simplify the square root by grouping pairs of the same prime factors:
13 * √(3 * 3 * 3)
= 13 * √(3^3)
= 13 * 3 * √3
= 39√3
Therefore, 13√27 simplifies to 39√3.