What is the value of 4√2 + 2√32?
Answer (2)
The expression 4 2 + 2 32 simplifies to 12 2 by combining like terms. First, 2 32 simplifies to 8 2 , and then both terms can be added together. Thus, the final result is 12 2 .
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To solve the expression 4 2 + 2 32 , we first need to simplify each part, especially the 2 32 term, to see if it can be expressed in terms of 2 .
Simplify 32 :
We can express 32 as a product of squares. Notice that 32 = 16 × 2 .
So, 32 = 16 × 2 = 16 × 2 .
Since 16 = 4 , we have 32 = 4 2 .
Substitute back into the original expression:
Now replace 32 with its simplified form: 2 32 = 2 × 4 2 = 8 2 .
Combine the terms:
We now have a simplified expression: 4 2 + 8 2 .
Since these are like terms, we can simply add the coefficients (4 and 8): 4 2 + 8 2 = ( 4 + 8 ) 2 = 12 2 .
So, the final answer to the problem is 12 2 .
