Powers and Roots: Solving the problem

To solve the expression $6+\sqrt{64}-4=$, we need to follow the order of operations (PEMDAS/BODMAS):

• P: Parentheses (or Brackets)
• E: Exponents (or Orders, i.e., powers and roots, etc.)
• MD: Multiplication and Division (left-to-right)
• AS: Addition and Subtraction (left-to-right)

In this expression, we first need to evaluate the square root since it falls under the exponent category:

$\sqrt{64} = 8$

Next, we substitute the computed value back into the expression:

$6+8-4$

We then perform the addition and subtraction from left to right:

$6+8 = 14$

$14-4 = 10$

Thus, the final answer is:

$10$

Let's recall the order of operations:

1. Parentheses

2. Exponents and Roots

3. Multiplication and Division

4. Addition and Subtraction

There are no parentheses in this problem, so we'll start with exponents:

3*3+3² =

3*3+9 =

Let's continue to the next step, multiplication operations:

3*3+9 =

9 + 9 =

Now we're left with just a simple addition problem:

9+9= 18

And that's the solution!

First, evaluate the square root: $\sqrt{49}=7$.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Addition: $7 + 7 = 14$

2. Subtraction: $14 - 5 = 9$

So, the correct answer is $9$.

First, evaluate the square root: $\sqrt{81}=9$.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Multiplication: $3 \times 2 = 6$

2. Addition: $6 + 9 = 15$

So, the correct answer is $15$.

First, evaluate the square root: $\sqrt{16}=4$.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Multiplication: $4 \times 3 = 12$

2. Subtraction: $8 - 12 = -4$

So, the correct answer is $-4$.

First, compute the power: $5^2 = 25$.

Next, divide: $25 \div 5 = 5$.

Finally, subtract: $10 - 5 = 5$.

First, compute the power: $4^2 = 16$.

Next, divide: $16 \div 2 = 8$.

Finally, subtract: $15 - 8 = 7$.

First, compute the power: $3^3 = 27$.

Next, divide: $27 \div 3 = 9$.

Finally, subtract: $20 - 9 = 11$.

First, follow the order of operations (BODMAS/BIDMAS):

Step 1: Calculate the exponent:
$4^2 = 16$

Step 2: Perform the multiplication:
$3 \times 2 = 6$

Step 3: Perform the addition and subtraction from left to right:
$8 + 6 - 16 = 14 - 16 = -2$

The correct result is: $-2$.

First, follow the order of operations (BODMAS/BIDMAS):

Step 1: Calculate the exponent:
$2^2 = 4$

Step 2: Perform the multiplication:
$5 \times 4 = 20$

Step 3: Perform the addition and subtraction from left to right:
$6 - 3 + 20 = 23$

The correct result is: $23$.

First, solve the square root: $\sqrt{49} = 7$.

Next, multiply 7 by 3: $7 \times 3 = 21$.

Finally, add 4 to 21: $4 + 21 = 25$.

Start by calculating the power: $5^2 = 25$.

Then, calculate the square root: $\sqrt{16} = 4$.

Subtract 4 from 25: $25 - 4 = 21$.

Finally, add 2: $21 + 2 = 23$.

First, calculate the powers:

$3^2 = 9$

$4^2 = 16$

Now substitute these values into the expression:

$81:3^2+4^2 = 81:9+16$

Perform the division:

$81 \div 9 = 9$

Finally, add the result to 16:

$9 + 16 = 25$

First, calculate the powers:

$2^3 = 8$

$5^2 = 25$

Now substitute these values into the expression:

$64:2^3+5^2 = 64:8+25$

Perform the division:

$64 \div 8 = 8$

Finally, add the result to 25:

$8 + 25 = 33$

In the first stage, let's calculate the powers of each of the terms:

$5^3=5\times5\times5=25\times5=125$

$5^2=5\times5=25$

$2^3=2\times2\times2=4\times2=8$

Now let's write the resulting expression:

$125:25\times8=$

Since the only operations in the expression are multiplication and division, we will solve the expression from left to right

In other words, we will divide first and then multiply:

$125:25=5$

$5\times8=40$

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: $1552$.

The given expression is: $\sqrt{36}\times\sqrt{49}+7^2\times2$.

First, calculate the square roots: $\sqrt{36} = 6$ and $\sqrt{49} = 7$.

Multiply the square roots: $6 \times 7 = 42$.

Next, calculate the square: $7^2 = 49$.

Multiply the result by 2: $49 \times 2 = 98$.

Finally, add the two results: $42 + 98 = 150$.

Thus, the answer is: $150$.

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.

Let's solve this problem step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

1. First, let's focus on what's inside the parentheses: $\sqrt{36}+9$

2. We need to evaluate the square root first:

• $\sqrt{36} = 6$ (because $6 \times 6 = 36$)

3. Now our expression looks like this: $2\times(6+9)$

4. Next, we perform the addition inside the parentheses:

• $6 + 9 = 15$

5. Our expression is now: $2\times15$

6. Finally, we perform the multiplication:

• $2 \times 15 = 30$

Therefore, $2\times(\sqrt{36}+9) = 30$

This matches the provided correct answer of 30.

We begin by solving the expression inside the parentheses $(20-3\times2^2)^2$. According to the order of operations (PEMDAS/BODMAS), we first handle any calculations inside parentheses and deal with exponents before performing multiplication, division, addition, or subtraction.

• Step 1: Solve the exponent inside the parentheses.

We have $2^2$, which equals $4$. Thus, the expression now is:



$(20-3\times4)^2$



• Step 2: Perform the multiplication inside the parentheses.

Multiply $3$ by $4$ to get $12$. The expression now simplifies to:



$(20-12)^2$



• Step 3: Perform the subtraction inside the parentheses.

Subtract $12$ from $20$. We get $8$. The expression now simplifies to:



$(8)^2$



• Step 4: Finally, solve the remaining exponent.

$8^2$ equals $64$.



Thus, $(20-3\times2^2)^2$ equals $64$.