Powers and Roots: Large Numbers

To solve the expression $143-\sqrt{121}+18$, we need to follow the order of operations, which dictate that we should simplify any expressions under a square root first, followed by subtraction and addition.

Step 1: Simplify the square root:

• Calculate the square root: $\sqrt{121}$.
• The square root of 121 is 11, because $11 \times 11 = 121$.

Now, substitute back into the expression:

• The expression becomes: $143 - 11 + 18$.

Step 2: Perform the subtraction:

• Calculate $143 - 11$.
• This equals 132, because subtracting 11 from 143 yields 132.

Step 3: Perform the addition:

• Now add 18 to the result of the subtraction: $132 + 18$.
• The result is 150, because adding 18 to 132 equals 150.

Therefore, the final answer is $150$.

To solve the expression $81+\sqrt{81}+10$, we need to follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Here, the expression contains a square root, which is a type of exponent operation. Therefore, we will handle the square root first:

• Find the square root of 81, which is calculated as follows: $\sqrt{81} = 9$.

Now substitute the result back into the original expression:

$81 + 9 + 10$

Next, perform the addition operations from left to right:

• First, add 81 and 9: $81 + 9 = 90$.
• Then, add the result to 10: $90 + 10 = 100$.

Therefore, the final result of the expression $81+\sqrt{81}+10$ is:

$100$

The given expression is: $\sqrt{16}\times\sqrt{25}+8^3\times3$.

First, calculate the square roots: $\sqrt{16} = 4$ and $\sqrt{25} = 5$.

Multiply the square roots: $4 \times 5 = 20$.

Next, calculate the cube: $8^3 = 512$.

Multiply the result by 3: $512 \times 3 = 1536$.

Finally, add the two results: $20 + 1536 = 1556$.

Thus, the answer is: $1556$.

Previously mentioned in the order of arithmetic operations, exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the terms with exponents inside the parentheses first) :

$5:(13^2-12^2) =5:(169-144) =5:25=\frac{5}{25}$where in the second step we simplified the expression in parentheses, and in the next step we wrote the division operation as a fraction,

Then we'll perform the division (we'll actually reduce the fraction):

$\frac{\not{5}}{\not{25}}=\frac{1}{5}$Therefore the correct answer is answer C.

To solve the expression $(18-10)^2+3^3$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Step 1: Parentheses
  First, solve the expression inside the parentheses: $18-10$.
  $18-10 = 8$

• Step 2: Exponents
  Next, apply the exponents to the numbers:
  $(8)^2$ and $3^3$.
  $8^2 = 64$
  $3^3 = 27$

• Step 3: Addition
  Finally, add the results of the exponentiations:
  $64 + 27$
  $64 + 27 = 91$

Thus, the final answer is $91$.

The given expression is $18^2-(100+\sqrt{9})$

We need to follow the order of operations (PEMDAS/BODMAS), which stands for:

• Parentheses

• Exponents (i.e., powers and square roots, etc.)

• MD Multiplication and Division (left-to-right)

• AS Addition and Subtraction (left-to-right)

Let's solve step by step:

Step 1: Evaluate the exponent and the square root in the expression:

• $18^2 = 324$

• $\sqrt{9} = 3$

So, the expression becomes $324 - (100 + 3)$

Step 2: Simplify the parentheses:

• $100+3=103$

So, the expression becomes $324 - 103$

Step 3: Subtract:

• $324-103=221$

Therefore, the value of the expression $18^2-(100+\sqrt{9})$ is 221.