Sqrt(36x^37)
√(36x^37)
To simplify this expression, we can break down the square root into its factors:
√(36 * x^37)
Next, we can simplify the perfect square factor, 36:
√(6^2 * x^37)
Now, we can apply the rules of square roots to separate the factors:
√6^2 * √x^37
The square root of 6^2 is 6, and the square root of x^37 is x^18.5 (since the power is an odd number):
6x^18.5
Hence, the simplified expression is 6x^18.5.
To simplify the expression sqrt(36x^37):
Step 1: Rewrite 36 as its prime factorization: 36 = 2^2 * 3^2.
Step 2: Utilize the property of square roots, which states that sqrt(a * b) = sqrt(a) * sqrt(b).
Step 3: Apply the property to the expression sqrt(36x^37):
sqrt(36x^37) = sqrt(2^2 * 3^2 * x^37)
= sqrt(2^2) * sqrt(3^2) * sqrt(x^37)
= 2 * 3 * sqrt(x^37)
= 6 * sqrt(x^37)
= 6 * x^(37/2)
= 6x^(37/2)