simplify to the lowest term
Square root of 40x^3
√(40x^3)
= √4*√10*√x^2*√x
= 2x√(10x)
To simplify the square root of 40x^3 to its lowest terms, you need to factor out perfect squares from the expression under the square root.
Step 1: Determine the prime factors of 40x^3.
40 = 2 * 2 * 2 * 5
x^3 = x * x * x
Step 2: Divide the exponents of prime factors by 2 (since we are taking the square root).
sqrt(40x^3) = sqrt(2^2 * 2^2 * 2 * 5 * x * x * x)
= 2 * 2 * x * sqrt(10x)
= 4x * sqrt(10x)
Therefore, the simplified form of the square root of 40x^3 is 4x * sqrt(10x).