Answer :
Sure! Let's break down and solve the problem step by step.
We are given three expressions to calculate, compare, and order:
1. [tex]\(35.8 - \sqrt{121}\)[/tex]
2. [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex]
3. [tex]\(6.3 \times \sqrt{64}\)[/tex]
Let's evaluate each expression one by one.
### Step 1: Evaluate each expression
#### Expression 1: [tex]\(35.8 - \sqrt{121}\)[/tex]
- First, we calculate [tex]\(\sqrt{121}\)[/tex]. The square root of 121 is 11.
- Next, we subtract 11 from 35.8.
[tex]\[
35.8 - 11 = 24.8
\][/tex]
- So, the value of the first expression is 24.8.
#### Expression 2: [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex]
- First, we calculate [tex]\(\sqrt{225}\)[/tex]. The square root of 225 is 15.
- Next, we add [tex]\(10 \frac{1}{4}\)[/tex] (which is [tex]\(10.25\)[/tex]) to 15.
[tex]\[
15 + 10.25 = 25.25
\][/tex]
- So, the value of the second expression is 25.25.
#### Expression 3: [tex]\(6.3 \times \sqrt{64}\)[/tex]
- First, we calculate [tex]\(\sqrt{64}\)[/tex]. The square root of 64 is 8.
- Next, we multiply 6.3 by 8.
[tex]\[
6.3 \times 8 = 50.4
\][/tex]
- So, the value of the third expression is 50.4.
### Step 2: Compare and order the expressions
Now we have the values of all three expressions:
- Expression 1: 24.8
- Expression 2: 25.25
- Expression 3: 50.4
We need to order these values from smallest to largest.
The ordered values are:
1. 24.8 (Expression 1)
2. 25.25 (Expression 2)
3. 50.4 (Expression 3)
### Final Answer:
The ordered expressions are:
- First: [tex]\(35.8 - \sqrt{121}\)[/tex] with the value of 24.8
- Second: [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex] with the value of 25.25
- Third: [tex]\(6.3 \times \sqrt{64}\)[/tex] with the value of 50.4
So, the expressions ordered from smallest to largest are:
1. [tex]\(35.8 - \sqrt{121}\)[/tex]
2. [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex]
3. [tex]\(6.3 \times \sqrt{64}\)[/tex]
I hope this helps! If you have any further questions, feel free to ask.
We are given three expressions to calculate, compare, and order:
1. [tex]\(35.8 - \sqrt{121}\)[/tex]
2. [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex]
3. [tex]\(6.3 \times \sqrt{64}\)[/tex]
Let's evaluate each expression one by one.
### Step 1: Evaluate each expression
#### Expression 1: [tex]\(35.8 - \sqrt{121}\)[/tex]
- First, we calculate [tex]\(\sqrt{121}\)[/tex]. The square root of 121 is 11.
- Next, we subtract 11 from 35.8.
[tex]\[
35.8 - 11 = 24.8
\][/tex]
- So, the value of the first expression is 24.8.
#### Expression 2: [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex]
- First, we calculate [tex]\(\sqrt{225}\)[/tex]. The square root of 225 is 15.
- Next, we add [tex]\(10 \frac{1}{4}\)[/tex] (which is [tex]\(10.25\)[/tex]) to 15.
[tex]\[
15 + 10.25 = 25.25
\][/tex]
- So, the value of the second expression is 25.25.
#### Expression 3: [tex]\(6.3 \times \sqrt{64}\)[/tex]
- First, we calculate [tex]\(\sqrt{64}\)[/tex]. The square root of 64 is 8.
- Next, we multiply 6.3 by 8.
[tex]\[
6.3 \times 8 = 50.4
\][/tex]
- So, the value of the third expression is 50.4.
### Step 2: Compare and order the expressions
Now we have the values of all three expressions:
- Expression 1: 24.8
- Expression 2: 25.25
- Expression 3: 50.4
We need to order these values from smallest to largest.
The ordered values are:
1. 24.8 (Expression 1)
2. 25.25 (Expression 2)
3. 50.4 (Expression 3)
### Final Answer:
The ordered expressions are:
- First: [tex]\(35.8 - \sqrt{121}\)[/tex] with the value of 24.8
- Second: [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex] with the value of 25.25
- Third: [tex]\(6.3 \times \sqrt{64}\)[/tex] with the value of 50.4
So, the expressions ordered from smallest to largest are:
1. [tex]\(35.8 - \sqrt{121}\)[/tex]
2. [tex]\(\sqrt{225} + 10 \frac{1}{4}\)[/tex]
3. [tex]\(6.3 \times \sqrt{64}\)[/tex]
I hope this helps! If you have any further questions, feel free to ask.
