Rewrite the radical using common factors.

\(\displaystyle \sqrt{-72}=\sqrt{-1}\cdot\sqrt{9}\cdot\sqrt{4}\cdot \sqrt{2}\)

Recall that \(\displaystyle \sqrt{-1}\) is equivalent to the imaginary term \(\displaystyle i\).

Simplify the roots.

\(\displaystyle i\cdot 3\cdot 2\cdot \sqrt2\)

The answer is:  \(\displaystyle 6i\sqrt2\)

Evaluate each square root.  The square root of the number is equal to a number multiplied by itself.

\(\displaystyle -\sqrt{121}+\sqrt{64}-\sqrt{16} =-11+8-4 =-7\)

The answer is:  \(\displaystyle -7\)

Simplify each radical.  A number inside the radical means that we are looking for a number times itself that will equal to that value inside the radical.

\(\displaystyle \sqrt{16}=4\)

\(\displaystyle \sqrt{36}=6\)

For a fourth root term, we are looking for a number that multiplies itself four times to get the number inside the radical.

\(\displaystyle \sqrt[4]{16} =2\)

Replace the values and determine the sum.

\(\displaystyle \sqrt{16}+\sqrt{36}- \sqrt[4]{16} = 4+6-2 = 8\)

The answer is:  \(\displaystyle 8\)

Do not multiply the terms inside the radical.  Instead, the terms inside the radical can be simplified term by term.

\(\displaystyle \sqrt{144\times 25\times 36} = \sqrt{144}\times \sqrt{25}\times \sqrt{36}\)

Simplify each square root.

\(\displaystyle 12\times 5\times 6 = 360\)

The answer is:  \(\displaystyle 360\)

Solve by evaluating the square roots first.  

\(\displaystyle \sqrt{36} = 6\)

\(\displaystyle \sqrt{100}=10\)

Substitute the terms back into the expression.

\(\displaystyle 2\sqrt{36}-4\sqrt{100} = 2(6)-4(10) = 12-40= -28\)

The answer is:  \(\displaystyle -28\)

Evaluate each radical.  The square root of a certain number will output a number that will equal the term inside the radical when it's squared.

\(\displaystyle \sqrt{9}=3\)

\(\displaystyle \sqrt{64}=8\)

\(\displaystyle \sqrt{36+64} = \sqrt{100} =10\)

Replace all the terms.

\(\displaystyle \sqrt9+\sqrt{64}+\sqrt{36+64} = 3+8+10 = 21\)

The answer is:  \(\displaystyle 21\)

This expression is imaginary.  To simplify, we will need to factor out the imaginary term \(\displaystyle i=\sqrt{-1}\) as well as the perfect square.

\(\displaystyle \sqrt{-200} = \sqrt{-1}\cdot \sqrt{100}\cdot \sqrt2\)

Simplify the terms.

\(\displaystyle i\cdot 10\cdot \sqrt2\)

The answer is:  \(\displaystyle 10i\sqrt2\)

Evaluate each square root.  The square root identifies a number that multiplies by itself to equal the number inside the square root.

\(\displaystyle \sqrt{81}+\sqrt{225}-\sqrt{10000} = 9+15-100\)

Determine the sum.

The answer is:  \(\displaystyle -76\)

The negative numbers inside the radical indicates that we will have imaginary terms.

Recall that \(\displaystyle i=\sqrt{-1}\).

Rewrite the radicals using \(\displaystyle \sqrt{-1}\) as the common factor.

\(\displaystyle 2\sqrt{-64}-3\sqrt{-16} = 2\cdot \sqrt{-1}\cdot \sqrt{64}-3\cdot \sqrt{-1}\cdot\sqrt{16}\)

Replace the terms and evaluate the square roots.

\(\displaystyle 2\cdot i\cdot8 - 3 \cdot i \cdot4 =16i-12i = 4i\)

The answer is:  \(\displaystyle 4i\)

Evaluate by solving each square root first.  The square root of a number is a number that multiplies by itself to achieve the number inside the square root.

\(\displaystyle \sqrt{100} =10\)

\(\displaystyle \sqrt{64}=8\)

\(\displaystyle \sqrt{169} = 13\)

Rewrite the expression.

\(\displaystyle \sqrt{100}-\sqrt{64}-\sqrt{169} = 10-8-13\)

The answer is:  \(\displaystyle -11\)