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}$
In order to see if a radical is in simplified form, see if any of its factors are perfect squares (meaning that their square root will be an integer). We see that 150 has factors of 25 and 6. 25 is a perfect square, so we know that we can simplify:
$3b^{4}\sqrt {150} = 3b^{4} \times \sqrt {25} \times \sqrt {6} = 15b^{4} \sqrt {6}$
