Answer :
Sure, let's break down each expression step-by-step, calculate their values, and then compare and order them.
### Expression 1: [tex]\( 35.8 - \sqrt{121} \)[/tex]
1. Calculate the square root of 121:
[tex]\[
\sqrt{121} = 11
\][/tex]
2. Subtract this from 35.8:
[tex]\[
35.8 - 11 = 24.8
\][/tex]
So, the value of the first expression is [tex]\( 24.8 \)[/tex].
### Expression 2: [tex]\( \sqrt{225} + 10 \frac{1}{4} \)[/tex]
1. Calculate the square root of 225:
[tex]\[
\sqrt{225} = 15
\][/tex]
2. Convert the mixed number [tex]\( 10 \frac{1}{4} \)[/tex] to a decimal:
[tex]\[
10 \frac{1}{4} = 10 + \frac{1}{4} = 10.25
\][/tex]
3. Add these values together:
[tex]\[
15 + 10.25 = 25.25
\][/tex]
So, the value of the second expression is [tex]\( 25.25 \)[/tex].
### Expression 3: [tex]\( 6.3 \times \sqrt{64} \)[/tex]
1. Calculate the square root of 64:
[tex]\[
\sqrt{64} = 8
\][/tex]
2. Multiply this by 6.3:
[tex]\[
6.3 \times 8 = 50.4
\][/tex]
So, the value of the third expression is [tex]\( 50.4 \)[/tex].
### Ordering the Expressions
Now that we have all the values, we can order them from smallest to largest:
1. [tex]\( 24.8 \)[/tex]
2. [tex]\( 25.25 \)[/tex]
3. [tex]\( 50.4 \)[/tex]
Therefore, the ordered expressions are:
1. [tex]\( 35.8 - \sqrt{121} = 24.8 \)[/tex]
2. [tex]\( \sqrt{225} + 10 \frac{1}{4} = 25.25 \)[/tex]
3. [tex]\( 6.3 \times \sqrt{64} = 50.4 \)[/tex]
### Expression 1: [tex]\( 35.8 - \sqrt{121} \)[/tex]
1. Calculate the square root of 121:
[tex]\[
\sqrt{121} = 11
\][/tex]
2. Subtract this from 35.8:
[tex]\[
35.8 - 11 = 24.8
\][/tex]
So, the value of the first expression is [tex]\( 24.8 \)[/tex].
### Expression 2: [tex]\( \sqrt{225} + 10 \frac{1}{4} \)[/tex]
1. Calculate the square root of 225:
[tex]\[
\sqrt{225} = 15
\][/tex]
2. Convert the mixed number [tex]\( 10 \frac{1}{4} \)[/tex] to a decimal:
[tex]\[
10 \frac{1}{4} = 10 + \frac{1}{4} = 10.25
\][/tex]
3. Add these values together:
[tex]\[
15 + 10.25 = 25.25
\][/tex]
So, the value of the second expression is [tex]\( 25.25 \)[/tex].
### Expression 3: [tex]\( 6.3 \times \sqrt{64} \)[/tex]
1. Calculate the square root of 64:
[tex]\[
\sqrt{64} = 8
\][/tex]
2. Multiply this by 6.3:
[tex]\[
6.3 \times 8 = 50.4
\][/tex]
So, the value of the third expression is [tex]\( 50.4 \)[/tex].
### Ordering the Expressions
Now that we have all the values, we can order them from smallest to largest:
1. [tex]\( 24.8 \)[/tex]
2. [tex]\( 25.25 \)[/tex]
3. [tex]\( 50.4 \)[/tex]
Therefore, the ordered expressions are:
1. [tex]\( 35.8 - \sqrt{121} = 24.8 \)[/tex]
2. [tex]\( \sqrt{225} + 10 \frac{1}{4} = 25.25 \)[/tex]
3. [tex]\( 6.3 \times \sqrt{64} = 50.4 \)[/tex]
