1. Sqrt 14r * 2 sqrt 4r
Is this 4r sqrt 14?
2. (sqrt 64 y^10 h^5)/(sqrt 16 y^12 h^3)
Is this (sqrt 4h^2)/(y^2)
#1 is correct
#2 is correct, but you left out the last step:
2h/y
I don't understand what you mean by the last step. Is the answer supposed to be 2h/y?
I get it--the square root.
To simplify these expressions, we can apply the rules of simplifying square roots.
1. Sqrt(14r) * 2 sqrt(4r)
To simplify, we can combine the square roots and multiply the coefficients:
sqrt(14r) * 2 sqrt(4r) = 2 sqrt(14r) sqrt(4r)
Since the square root of 4 is 2, we can simplify further:
2 sqrt(14r) sqrt(4r) = 2 * 2 sqrt(14r) sqrt(r)
Using the property sqrt(a) * sqrt(b) = sqrt(a * b), we can simplify further:
2 * 2 sqrt(14r) sqrt(r) = 4 sqrt(14r * r)
Now, multiplying r and r gives us r^2:
4 sqrt(14r * r) = 4 sqrt(14r^2)
Thus, the simplified expression is:
4 sqrt(14r^2)
2. (sqrt(64 y^10 h^5)) / (sqrt(16 y^12 h^3))
To simplify this expression, we can again combine the square roots and divide them:
(sqrt(64 y^10 h^5)) / (sqrt(16 y^12 h^3)) = sqrt(64 y^10 h^5 / (16 y^12 h^3))
Using the property sqrt(a/b) = sqrt(a) / sqrt(b), we can simplify further:
sqrt(64 y^10 h^5 / (16 y^12 h^3)) = sqrt(64 h^5 / (16 h^3)) * sqrt(y^10 / y^12)
Since 64/16 = 4 and h^5 / h^3 = h^2, we can simplify further:
sqrt(64 h^5 / (16 h^3)) * sqrt(y^10 / y^12) = sqrt(4h^2) * sqrt(y^10 / y^12)
Finally, simplifying the square roots gives us:
sqrt(4h^2) * sqrt(y^10 / y^12) = 2h * sqrt(y^10 / y^12)
Since y^10 / y^12 = 1 / y^2, we can simplify further:
2h * sqrt(y^10 / y^12) = 2h * sqrt(1 / y^2)
Using the property sqrt(1/a) = 1 / sqrt(a), we get:
2h * sqrt(1 / y^2) = 2h * (1 / y)
Thus, the simplified expression is:
(2h) / y