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:  $\displaystyle -11$