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Answer :
Let's break down the given expression step by step:
1. Convert the Mixed Number to a Decimal:
The first step is to convert the mixed number [tex]\(625 \frac{3}{8}\)[/tex] into a decimal. You do this by adding [tex]\(625\)[/tex] to the fractional part [tex]\(\frac{3}{8}\)[/tex].
[tex]\[
625 + \frac{3}{8} = 625.375
\][/tex]
2. Evaluate the Square Root:
Next, we need to find the value of [tex]\(5^{\frac{1}{2}}\)[/tex]. The exponent [tex]\(\frac{1}{2}\)[/tex] indicates the square root of 5.
[tex]\[
5^{\frac{1}{2}} = \sqrt{5} \approx 2.236
\][/tex]
3. Complete the Multiplication:
Now, we multiply the decimal result from the first step with the square root found in the second step, and then multiply by [tex]\(25\)[/tex]:
[tex]\[
625.375 \times 2.236 \times 25
\][/tex]
This equals approximately:
[tex]\[
\approx 34959.525
\][/tex]
Thus, when you simplify the expression [tex]\(625 \frac{3}{8} \times 5^{\frac{1}{2}} \times 25\)[/tex], you get approximately [tex]\(34959.525\)[/tex].
1. Convert the Mixed Number to a Decimal:
The first step is to convert the mixed number [tex]\(625 \frac{3}{8}\)[/tex] into a decimal. You do this by adding [tex]\(625\)[/tex] to the fractional part [tex]\(\frac{3}{8}\)[/tex].
[tex]\[
625 + \frac{3}{8} = 625.375
\][/tex]
2. Evaluate the Square Root:
Next, we need to find the value of [tex]\(5^{\frac{1}{2}}\)[/tex]. The exponent [tex]\(\frac{1}{2}\)[/tex] indicates the square root of 5.
[tex]\[
5^{\frac{1}{2}} = \sqrt{5} \approx 2.236
\][/tex]
3. Complete the Multiplication:
Now, we multiply the decimal result from the first step with the square root found in the second step, and then multiply by [tex]\(25\)[/tex]:
[tex]\[
625.375 \times 2.236 \times 25
\][/tex]
This equals approximately:
[tex]\[
\approx 34959.525
\][/tex]
Thus, when you simplify the expression [tex]\(625 \frac{3}{8} \times 5^{\frac{1}{2}} \times 25\)[/tex], you get approximately [tex]\(34959.525\)[/tex].
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