How do you simplify #5sqrt(2y^2)-3ysqrt8#?

Question

Genesis Allen · Accepted Answer

#= -ysqrt2#

Take out as many roots as you can.

#5sqrt(2color(red)(y^2)) - 3ysqrt(color(blue)(4)xx2)" "larr (8 = 4xx2)#

#=5color(red)(y)sqrt2-3 xx color(blue)(2)ysqrt2#

#=5ysqrt2 -6ysqrt2" "larr# these are like terms

#= -ysqrt2#

Kennedy Adams · Answer

undefined To simplify 5sqrt(2y^2)-3ysqrt8, we can break it down into separate terms and simplify each term individually.

First, let's simplify 5sqrt(2y^2). Since the square root of a product is equal to the product of the square roots, we can rewrite this as 5sqrt(2)*sqrt(y^2). The square root of y^2 is simply y, so this becomes 5sqrt(2)*y.

Next, let's simplify -3ysqrt8. Again, using the property mentioned earlier, we can rewrite this as -3y*sqrt(8). The square root of 8 can be simplified as sqrt(4*2), which is equal to 2sqrt(2). Therefore, -3y*sqrt(8) becomes -3y*2sqrt(2), which simplifies to -6ysqrt(2).

Combining the simplified terms, we have 5sqrt(2)*y - 6ysqrt(2). Since both terms have a common factor of y and sqrt(2), we can factor them out. This gives us (5 - 6)y*sqrt(2), which simplifies to -y*sqrt(2).

Therefore, the simplified form of 5sqrt(2y^2)-3ysqrt8 is -y*sqrt(2).