Correct answer: A

The correct answer is $2.65$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: $2.65^2=7.0225$, so 2.65 is close to the exact square root of 7.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: B

The correct answer is $7.42$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: $7.42^2=55.0564$, which is close to 55.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: C

The correct answer is $2.15$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: $2.15^3=9.938375$, which is close to 10.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: D

The correct answer is $4.48$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: $4.48^3\approx89.9$, so 4.48 is a reasonable estimate.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: A

The correct answer is $\sqrt{6}$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: Since 6 is not a perfect square, $\sqrt{6}$ is irrational.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: B

The correct answer is $\sqrt[3]{27}$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: $\sqrt[3]{27}=3$, and 3 is an integer and therefore rational.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: C

The correct answer is $\sqrt{0}=0$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: Zero is a perfect square because $0^2=0$, so its principal square root is 0.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: D

The correct answer is $\sqrt{-9}$ is not a real number..

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: No real number squared equals -9 because the square of every real number is nonnegative.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: A

The correct answer is $\frac{17}{4}$.

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: $\frac{17}{4}=4.25$, while $\sqrt{18}\approx4.243$ and $\sqrt{15}\approx3.873$.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.

Correct answer: B

The correct answer is The inverse operation shows whether the estimate is close to the original radicand..

1. Identify the root or radical: Determine whether the problem asks for a square root, cube root, perfect power, estimate, simplification, comparison, or equation solution.
2. Use nearby perfect powers: If the estimated square root is close, its square should be close to the radicand; the same idea applies to cube roots.
3. Check the result: Square or cube the answer when possible, verify the sign, and keep exact radical form unless an approximation is requested.