Question

Find the simplified product 2 square root 5x^3(-3 square root 10x^2

Answer 1

The simplified product of $2\sqrt{5x^{3} }$ and -3$\sqrt{10x^{2} }$ is -30$x^{5/2} \sqrt{2}$.

Given Two expressions: -3$\sqrt{10x^{2} }$ and 2$\sqrt{5x^{3} }$.

We have to multiply both the expressions and it can be done as under:

-3$\sqrt{10x^{2} }$ *2$\sqrt{5x^{3} }$

Firstly we have to multiply -3 with 2 to get

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

Then we have to find square root of x cube and x square which is x to the power 3/2 and x to the power 1.

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

Now we have to multiply both the numbers in the root to get the answer;

=-6$x^{5/2} \sqrt{50}$

Square root of 50 is 5 root 2.

=-6*5$\sqrt{2}$$x^{5/2}$

=-30$\sqrt{2}$$x^{5/2}$

Hence the simplified product is -30$\sqrt{2}$$x^{5/2}$.

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