Calculate. $(10.4)^2=$
Answer (2)
Calculate the square of 10.4: ( 10.4 ) 2 = 10.4 × 10.4 .
Break down the multiplication: 100 + 4 + 4 + 0.16 .
Sum the values: 100 + 4 + 4 + 0.16 = 108.16 .
The final answer is: 108.16 .
Explanation
Understanding the Problem We need to calculate ( 10.4 ) 2 and choose the correct answer from the given options: 20.16, 100.16, 20.8, 108.16. To do this, we will multiply 10.4 by itself.
Setting up the Calculation Let's calculate ( 10.4 ) 2 :
( 10.4 ) 2 = 10.4 × 10.4
Performing the Calculation We can perform this multiplication manually or use a calculator. Let's break it down: ( 10.4 ) 2 = ( 10 + 0.4 ) × ( 10 + 0.4 ) = 10 × 10 + 10 × 0.4 + 0.4 × 10 + 0.4 × 0.4 = 100 + 4 + 4 + 0.16 = 108 + 0.16 = 108.16
Comparing with Options Now we compare our result, 108.16, with the given options: 20.16, 100.16, 20.8, 108.16. The correct answer is 108.16.
Final Answer Therefore, ( 10.4 ) 2 = 108.16 .
Examples
Calculating squares is useful in many real-life situations. For example, if you want to find the area of a square garden with sides of 10.4 meters, you would calculate ( 10.4 ) 2 to find the area in square meters. This concept is also used in physics to calculate energy, such as kinetic energy, which involves squaring the velocity.
The calculation of ( 10.4 ) 2 results in 108.16. This is obtained by multiplying 10.4 by itself, which can be expanded using the distributive property. Therefore, ( 10.4 ) 2 = 108.16 .
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