Question

square root of 3x^4 times square root of 5x^2 times square root of 10.

Multiply and remove all perfect squares from inside the square roots. Assume x is positive.

Answer 1

Answer:

Step-by-step explanation:

As long as the indices are the same for all the radicals, you can multiply them together. Our index for each of these is 2 (square root) so we multiply them all together and put it under 1 square root sign (radical):

$\sqrt{150x^6$  The largest perfect square in 150 is 25, and the 6th power on the x needs just to be rewritten in terms of an exponent of 2 to give us:

$\sqrt{25*6*(x^3)^2}$ and pull out the perfect squares to get

$5x^3\sqrt{6}$

Answer 2

Answer:

$5x^3\sqrt{6}$

Step-by-step explanation:

We need to simplify

$\sqrt{3x^4}\times\sqrt{5x^2}\times\sqrt{10}$

Right away we can take out the perfect squares. Remember a perfect square is the result of multiplying any value by itself.

$= x^2\sqrt{3}\times x\sqrt{5}\times\sqrt{10} \\= x^3\sqrt{3\times 5 \times 10}\\= x^3\sqrt{3 \times 5 \times 5 \times 2 }\\= 5x^3\sqrt{6}$