Question
b) \( 14.5^{2}+0.714^{2} \)
Ask by Johnson Cummings.
Dec 27,2024 17:57
UpStudy AI Solution
Tutor-Verified Answer
Answer
The result is approximately 210.76.
Solution
Calculate or simplify the expression \( 14.5^2+0.714^2 \).
Calculate the value by following steps:
- step0: Calculate:
\(14.5^{2}+0.714^{2}\)
- step1: Convert the expressions:
\(\left(\frac{29}{2}\right)^{2}+0.714^{2}\)
- step2: Convert the expressions:
\(\left(\frac{29}{2}\right)^{2}+\left(\frac{357}{500}\right)^{2}\)
- step3: Simplify:
\(\frac{29^{2}}{2^{2}}+\frac{357^{2}}{500^{2}}\)
- step4: Evaluate the power:
\(\frac{841}{4}+\frac{357^{2}}{500^{2}}\)
- step5: Reduce fractions to a common denominator:
\(\frac{841\times 62500}{4\times 62500}+\frac{357^{2}}{500^{2}}\)
- step6: Multiply the numbers:
\(\frac{841\times 62500}{250000}+\frac{357^{2}}{500^{2}}\)
- step7: Rewrite the expression:
\(\frac{841\times 62500}{500^{2}}+\frac{357^{2}}{500^{2}}\)
- step8: Transform the expression:
\(\frac{841\times 62500+357^{2}}{500^{2}}\)
- step9: Multiply the numbers:
\(\frac{52562500+357^{2}}{500^{2}}\)
The result of \(14.5^{2}+0.714^{2}\) is approximately 210.76.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
Did you know that squaring numbers can be traced back to ancient civilizations? The Babylonians and Egyptians used geometric methods to find squares, laying the groundwork for our modern understanding of squares in mathematics. Their methods show how integral arithmetic was in the development of early cultures!
On a practical note, when calculating \(14.5^2 + 0.714^2\), be sure to use a calculator for precision, especially with decimals. A common mistake here is to misplace the decimal point when adding, leading to incorrect results. Double-checking your work will save you from a math mishap!
Related Questions
If 8 ft. boards of drywall cost $20 and 12 ft. boards cost $29, what is the minimum price for covering a 16 x 24 room with 12 ft. ceilings (entire room)?
Arithmetic
Jun 10, 2025
Xavier mixes \( \frac{4}{5} \) bucketsof coarse sand with \( 1 \frac{1}{5} \) buckets of cement to make a
special type of concrete. How many buckets of concrete will he make?
Tasneem is an intern at ZX Communications Agency. She earns R4 500 a month
\( 1.2 .1 \quad \) Write the number 4500 in scientific notation.
\( 1.2 .2 \quad \) Increase R4500 in the ratio \( 5: 6 .(2 \times 2) \)
Arithmetic
Mar 23, 2025
1) Pat bounces a basketball 25 times in 30 seconds. At that rate, approximately how
many times will Pat bounce the ball in 150 seconds?
Answer:
Arithmetic
Mar 23, 2025
