simplify square root of u¹⁸

To simplify the square root of u¹⁸, we can first express the exponent 18 as a product of two factors: 18 = 9 * 2.

Therefore, we can rewrite the square root of u¹⁸ as the square root of u⁹ * u².

Using the property of square roots, we can split the square root of a product into the product of the square root of each factor:

sqrt(u⁹ * u²) = sqrt(u⁹) * sqrt(u²).

The square root of u⁹ is u⁴.5 (since 9 divided by 2 is 4.5).
And the square root of u² is u.

So, sqrt(u⁹) * sqrt(u²) simplifies to u⁴.5 * u.

Combining the terms, we get the simplified form:

u⁴.5 * u = u⁵.5