Join the IDNLearn.com community and start finding the answers you need today. Discover reliable answers to your questions with our extensive database of expert knowledge.
Sagot :
Sure! Let's solve the given expression step-by-step:
Expression to solve:
[tex]\[ 952 + 3 \sqrt{2} \times \frac{252 + 2 \sqrt{2}}{12 + 2 \sqrt{3}} \][/tex]
Step 1: Simplify the numerator and denominator of the fraction.
The numerator is:
[tex]\[ 252 + 2 \sqrt{2} \][/tex]
Evaluating this:
[tex]\[ 252 + 2 \sqrt{2} \approx 254.82842712474618 \][/tex]
The denominator is:
[tex]\[ 12 + 2 \sqrt{3} \][/tex]
Evaluating this:
[tex]\[ 12 + 2 \sqrt{3} \approx 15.464101615137753 \][/tex]
Step 2: Compute the fraction value.
[tex]\[ \frac{252 + 2 \sqrt{2}}{12 + 2 \sqrt{3}} \approx \frac{254.82842712474618}{15.464101615137753} \approx 16.47870878417506 \][/tex]
Step 3: Multiply this value by [tex]\(3 \sqrt{2}\)[/tex].
First, evaluate [tex]\(3 \sqrt{2}\)[/tex]:
[tex]\[ 3 \sqrt{2} \approx 3 \times 1.4142135623730951 \approx 4.242640687119285 \][/tex]
Now multiply:
[tex]\[ 3 \sqrt{2} \times \frac{252 + 2 \sqrt{2}}{12 + 2 \sqrt{3}} \approx 4.242640687119285 \times 16.47870878417506 \approx 69.91324035893108 \][/tex]
Step 4: Add this result to 952.
[tex]\[ 952 + 69.91324035893108 \approx 1021.913240358931 \][/tex]
So, the final result of the given expression is:
[tex]\[ \boxed{1021.913240358931} \][/tex]
Expression to solve:
[tex]\[ 952 + 3 \sqrt{2} \times \frac{252 + 2 \sqrt{2}}{12 + 2 \sqrt{3}} \][/tex]
Step 1: Simplify the numerator and denominator of the fraction.
The numerator is:
[tex]\[ 252 + 2 \sqrt{2} \][/tex]
Evaluating this:
[tex]\[ 252 + 2 \sqrt{2} \approx 254.82842712474618 \][/tex]
The denominator is:
[tex]\[ 12 + 2 \sqrt{3} \][/tex]
Evaluating this:
[tex]\[ 12 + 2 \sqrt{3} \approx 15.464101615137753 \][/tex]
Step 2: Compute the fraction value.
[tex]\[ \frac{252 + 2 \sqrt{2}}{12 + 2 \sqrt{3}} \approx \frac{254.82842712474618}{15.464101615137753} \approx 16.47870878417506 \][/tex]
Step 3: Multiply this value by [tex]\(3 \sqrt{2}\)[/tex].
First, evaluate [tex]\(3 \sqrt{2}\)[/tex]:
[tex]\[ 3 \sqrt{2} \approx 3 \times 1.4142135623730951 \approx 4.242640687119285 \][/tex]
Now multiply:
[tex]\[ 3 \sqrt{2} \times \frac{252 + 2 \sqrt{2}}{12 + 2 \sqrt{3}} \approx 4.242640687119285 \times 16.47870878417506 \approx 69.91324035893108 \][/tex]
Step 4: Add this result to 952.
[tex]\[ 952 + 69.91324035893108 \approx 1021.913240358931 \][/tex]
So, the final result of the given expression is:
[tex]\[ \boxed{1021.913240358931} \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.