11. Roots, Radicals, and Complex Numbers

Simplify the following.

${}^4\sqrt{{(-x)}^4}$

Simplify the root.

${}^4\sqrt{256}$

Evaluate the following square root.

$\sqrt{144}$

Simplify the following.

${-}^8\sqrt{{(x+1)}^8}$

Use a calculator to evaluate the following and round to the nearest hundredths.

${-}^8\sqrt{\frac{45}{29}}$

Simplify the following.

${}^4\sqrt{x^4{y}^8}$

Determine if the given square root evaluates to a real number.

$-\sqrt{4}$

Simplify the root.

${-}^4\sqrt{10,000}$

Simplify the root.

${}^3\sqrt{-125}$

Evaluate the following square root.

$-\sqrt{121}$

Simplify the root.

${}^5\sqrt{243}$

Estimate the square root between two consecutive whole numbers.

$\sqrt{138}$

Simplify the following.

${}^4\sqrt{{(2-a)}^4}$

Evaluate the radical.

$\sqrt{{(-5)}^2}$

Simplify the following.

${}^7\sqrt{{(-x-1)}^7}$