7(√6/32)
I came until 7(√192/32). How do I proceed from here?
192=32*6
I multiplied (√6/√32) by (√32/√32).
To simplify the expression 7(√192/32), you can start by simplifying the square root. The square root of 192 is not a perfect square, so you can break it down into its prime factors to simplify it further.
The prime factorization of 192 can be written as: 2 * 2 * 2 * 2 * 2 * 3 = 2^5 * 3.
So, √192 can be written as √(2^5 * 3).
Next, you can simplify the square root expression by taking out any perfect square factors from under the radical sign. In this case, there is a perfect square factor, 2^4, which equals 16. So, you can rewrite √192 as √(16 * 2 * 3).
Taking the square root of 16 gives you 4:
√(16 * 2 * 3) = 4√(2 * 3) = 4√6.
So, you now have the simplified expression: 7(4√6/32).
To proceed further, you can simplify the fraction 4√6/32 by dividing the numerator and the denominator by the greatest common divisor (GCD) of the two terms. In this case, the GCD of 4 and 32 is 4:
4√6/32 = (4/4)*(√6/8) = √6/8.
Therefore, the final simplified expression is √6/8.