What is the simplest form of the radical expression?32a−−√3−62a−−√3 show all work
To simplify the expression √(32a^3) - √(62a^3), we can first factor out the common factor from both terms inside the radicals:
√(32a^3) - √(62a^3)
= √(16 * 2 * a^2 * a) - √(31 * 2 * a^2 * a)
Next, we can simplify the square roots of the numbers that have perfect square factors:
= 4a√2 - √(31 * 2 * a^2 * a)
= 4a√2 - a√(62a)
Now, we have a common factor of "a" in both terms, so we can factor it out:
= a(4√2 - √(62a))
Therefore, the simplest form of the radical expression √(32a^3) - √(62a^3) is a(4√2 - √(62a)).