How do you multiply #xsqrt(10x)*7sqrt(15x)#?

Question

Kennedy Adams · Accepted Answer

The result is #35x^2sqrt6#.

Use the radical multiplication and simplification rules: Multiplication: #sqrta*sqrtb=sqrt(ab)# Simplification: #sqrt(a^2)=a# For this problem, first, multiply the radicals (in blue) and their coefficients (in red) together: #color(white)=color(red)xcolor(blue)sqrt(10x)*color(red)7color(blue)sqrt(15x)# #=color(red)x*color(blue)sqrt(10x)*color(red)7*color(blue)sqrt(15x)# #=color(red)x*color(red)7*color(blue)sqrt(10x)*color(blue)sqrt(15x)# #=color(red)(7x)*color(blue)sqrt(10x)*color(blue)sqrt(15x)# #=color(red)(7x)*color(blue)sqrt(10x*15x)# #=color(red)(7x)*color(blue)sqrt(10*15*x*x)# #=color(red)(7x)\*color(blue)sqrt(150*x*x)# #=color(red)(7x)*color(blue)sqrt(150*x^2)# Next, use the multiplication rule backwards: #color(white)=color(red)(7x)*color(blue)sqrt(150*x^2)# #=color(red)(7x)*color(blue)sqrt(150)*color(blue)(sqrt(x^2))# Now, use the simplification rule: #color(white)=color(red)(7x)*color(blue)sqrt(150)*color(blue)(sqrt(x^2))# #=color(red)(7x)*color(blue)sqrt(150)*color(red)x# #=color(red)(7x)*color(red)x*color(blue)sqrt(150)# #=color(red)(7x^2)*color(blue)sqrt(150)# Technically, this answer is correct, but it can be simplified further by factoring #150# and then using the simplification rule backward again: #color(white)=color(red)(7x^2)*color(blue)sqrt(150)# #=color(red)(7x^2)*color(blue)sqrt(6*25)# #=color(red)(7x^2)*color(blue)sqrt6*color(blue)sqrt25# #=color(red)(7x^2)*color(blue)sqrt6*color(blue)sqrt(5^2)# #=color(red)(7x^2)*color(blue)sqrt6*color(red)5# #=color(red)(7x^2)*color(red)5*color(blue)sqrt6# #=color(red)(35x^2)*color(blue)sqrt6# This answer is fully simplified.

Jace Anderson · Answer

undefined To multiply xsqrt(10x) and 7sqrt(15x), you can follow these steps:

1. Multiply the coefficients: 1 * 7 = 7.
2. Multiply the numbers inside the square roots: sqrt(10x) * sqrt(15x) = sqrt(150x^2).
3. Combine the results: 7 * sqrt(150x^2) = 7sqrt(150x^2).

Therefore, the product of xsqrt(10x) and 7sqrt(15x) is 7sqrt(150x^2).