Write as a sqrt, 2^3/2 x^3/2 y^5/2
(sqrt of 8)(sqrt of x^3)(sqrt of y^5)
√n = n^(1/2)
√(8 x^3 y^5)
To write the expression as a square root, we can simplify the exponent parts of each variable:
2^(3/2) means taking the square root (denoted by the exponent 1/2) of 2 raised to the power of 3. So, 2^(3/2) is equivalent to the square root of 2^3, which is √(2^3).
Similarly, x^(3/2) is the square root of x^3, which can be written as √(x^3).
Finally, y^(5/2) is the square root of y^5, which can be written as √(y^5).
Putting it all together, the expression becomes:
√(2^3) * √(x^3) * √(y^5)
Simplifying further, we can take the product of the square roots:
√(2^3 * x^3 * y^5)
Simplifying the exponents inside the square root:
√(8x^3y^5)
So, the expression, when written as a square root, is √(8x^3y^5).