Question

Wht is root {5} (root{5}root{2} )

Answer 1

The expression root{5} (root{5} root{2}) can be simplified using the product property of radicals, which states that the product of two square roots is equal to the square root of their product. Applying this property, we get:

root{5} (root{5} root{2}) = root{5 * 2} (root{5} * root{2})

Simplifying further, we get:

root{10} (root{10})

Now, applying the power property of radicals, which states that the square root of a number raised to a power is equal to the number raised to half of the power, we get:

root{10} (root{10}) = (10^(1/2))^(1/2) = 10^(1/4)

Therefore, the simplified form of the expression root{5} (root{5} root{2}) is 10^(1/4).

Explanation:

Answer 2

The expression can be simplified as follows:

root{5} (root{5}root{2} ) = root{5 x 5 x 2} = root{50} ≈ 7.071

Therefore, the value of the expression is approximately 7.071.