Simplify 4sqrt6/sqrt30
by rationalizing the denominator
first do this:
4√6/√30 =
4/√5
now multiply top and bottom by √5
4/√5 * √5/√5
= 4√5/5
To simplify the expression (4√6) / √30 by rationalizing the denominator, we need to eliminate the square root from the denominator (√30).
First, let's break down the square roots into their prime factorizations.
The prime factorization of 6 is: 2 * 3
The prime factorization of 30 is: 2 * 3 * 5
So, the expression becomes: (4√6) / (√(2 * 3 * 5))
Next, we want to find a factor inside the square root sign of the denominator that, when multiplied by itself, will result in an integer. In this case, we need to find a factor of 30 that can be written as the square root of a perfect square.
The factor 2 * 3 is already a perfect square (2 * 3)^2 = 2^2 * 3^2 = 36. Therefore, we can rewrite the square root of 30 as √(2 * 3 * 5) = √(36 * 5).
Now, we can simplify the expression: (4√6) / (√(36 * 5))
Using the property of square roots, we can separate the square root of a product into the product of the square roots: √(36 * 5) = √36 * √5 = 6√5.
Substituting the simplified denominator back into the expression, we get: (4√6) / (6√5).
Finally, we can simplify further by canceling out the common factors between the numerator and denominator. In this case, we can divide both the numerator and denominator by 2: (2 * 2√6) / (2 * 3√5).
Simplifying this expression gives us: 2√6 / 3√5.