The product of [tex](\sqrt{3x}+\sqrt{5} )\ (\sqrt{15x}+2\sqrt{30})[/tex] will be [tex]3x \sqrt{5}\ +\ 6 \sqrt{10x}}+ 5\sqrt{3x}}+\ 10\sqrt{6}[/tex] which is given in option [tex](b)[/tex] .
What is product ?
Product is the multiplication of two numbers or expressions or variables.
We have,
[tex](\sqrt{3x}+\sqrt{5} )\ (\sqrt{15x}+2\sqrt{30})[/tex]
Now,
Simplify and multiply;
[tex](\sqrt{3x})\ (\sqrt{15x}+2\sqrt{30})+\sqrt{5}\ (\sqrt{15x}+2\sqrt{30})[/tex]
⇒
[tex]\sqrt{3x}* \sqrt{15x}\ +\ \sqrt{3x} * 2\sqrt{30})+ \sqrt{5}\ *\ \sqrt{15x}+\ \sqrt{5}\ *\ 2\sqrt{30}[/tex]
Now, multiply
[tex]\sqrt{3x*15x}\ +\ 2 \sqrt{3x* 30}}+ \sqrt{5 *\ 15x}}+\ 2 \sqrt{5\ *\ 30}[/tex]
[tex]\sqrt{45x^2}\ +\ 2\sqrt{90x}}+ \sqrt{75x}}+\ 2\sqrt{150}[/tex]
Now, simplify which we can;
[tex]\sqrt{9*5*x^2}\ +\ 2\sqrt{9*10*x}}+ \sqrt{25*3*x}}+\ 2\sqrt{25*6}[/tex]
Now, take values out of root;
[tex]3x \sqrt{5}\ +\ 2*3 \sqrt{10x}}+ 5\sqrt{3x}}+\ 2*5\sqrt{6}[/tex]
[tex]3x \sqrt{5}\ +\ 6 \sqrt{10x}}+ 5\sqrt{3x}}+\ 10\sqrt{6}[/tex]
So, the product of given data is [tex]3x \sqrt{5}\ +\ 6 \sqrt{10x}}+ 5\sqrt{3x}}+\ 10\sqrt{6}[/tex], which is derived out by simplifying.
Hence, we can say that the product of [tex](\sqrt{3x}+\sqrt{5} )\ (\sqrt{15x}+2\sqrt{30})[/tex] will be [tex]3x \sqrt{5}\ +\ 6 \sqrt{10x}}+ 5\sqrt{3x}}+\ 10\sqrt{6}[/tex] which is given in option [tex](b)[/tex].
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