Answer
$ 15b^{4} \sqrt {6}$
Work Step by Step
We first separate the number and the variable into two separate square roots:
$ 3\sqrt {150} \times \sqrt {b^{8}} = 3 \sqrt {150} \times b^{4}$
We see if any of the factors of a radical are perfect squares (meaning that their square root will be an integer) to see if the radical is in its most simplified form. We see that 150 has factors of 25 and 6. 25 is a perfect square, so we know that we can simplify:
$3b^{4}\sqrt {150} = 3b^{4} \times \sqrt {25} \times \sqrt {6} = 15b^{4} \sqrt {6}$
