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The expression (11.98 * 11.98 + 11.98x + 0.02 * 0.02) will be a perfect square for x equal to:
- a)0.02
- b)0.2
- c)0.04
- d)0.4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The expression (11.98 *11.98 + 11.98x+ 0.02 *0.02) will be a perfect s...
Answer: Option C
Explanation:
Given expression = (11.98)2 + (0.02)2 + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x x = 2 x 11.98 x 0.02 or x = 0.04
Most Upvoted Answer
The expression (11.98 *11.98 + 11.98x+ 0.02 *0.02) will be a perfect s...
**Explanation:**
To determine if the expression (11.98 * 11.98 11.98x 0.02 * 0.02) is a perfect square, we need to simplify it and check if it can be written as the square of a single term. Let's break it down step by step:
Step 1: Simplify the expression
(11.98 * 11.98 11.98x 0.02 * 0.02)
= (143.7604 11.98x 0.0004)
Step 2: Factor out a common term
= (11.98 * 11.98) (11.98 * x) (0.02 * 0.02)
= (11.98)² (11.98 * x) (0.02)²
Step 3: Rearrange the terms
= (11.98)² (11.98 * x) (0.02)²
= [(11.98)² (0.02)²] (11.98 * x)
= (143.7604 0.0004) (11.98 * x)
= 144.1604 (11.98 * x)
Now, we can see that the expression can be written as the product of two terms: (144.1604) and (11.98 * x).
To determine if it is a perfect square, we need to check if (11.98 * x) can be written as the square of a single term.
Step 4: Simplify (11.98 * x)
Since we don't have any other information about the value of x, we cannot simplify it further. Therefore, we cannot write (11.98 * x) as the square of a single term.
Step 5: Conclusion
Since we cannot write (11.98 * x) as the square of a single term, the expression (11.98 * 11.98 11.98x 0.02 * 0.02) is not a perfect square.
Therefore, the correct answer is none of the options given (a) 0.02, (b) 0.2, (c) 0.04, or (d) 0.4.
To determine if the expression (11.98 * 11.98 11.98x 0.02 * 0.02) is a perfect square, we need to simplify it and check if it can be written as the square of a single term. Let's break it down step by step:
Step 1: Simplify the expression
(11.98 * 11.98 11.98x 0.02 * 0.02)
= (143.7604 11.98x 0.0004)
Step 2: Factor out a common term
= (11.98 * 11.98) (11.98 * x) (0.02 * 0.02)
= (11.98)² (11.98 * x) (0.02)²
Step 3: Rearrange the terms
= (11.98)² (11.98 * x) (0.02)²
= [(11.98)² (0.02)²] (11.98 * x)
= (143.7604 0.0004) (11.98 * x)
= 144.1604 (11.98 * x)
Now, we can see that the expression can be written as the product of two terms: (144.1604) and (11.98 * x).
To determine if it is a perfect square, we need to check if (11.98 * x) can be written as the square of a single term.
Step 4: Simplify (11.98 * x)
Since we don't have any other information about the value of x, we cannot simplify it further. Therefore, we cannot write (11.98 * x) as the square of a single term.
Step 5: Conclusion
Since we cannot write (11.98 * x) as the square of a single term, the expression (11.98 * 11.98 11.98x 0.02 * 0.02) is not a perfect square.
Therefore, the correct answer is none of the options given (a) 0.02, (b) 0.2, (c) 0.04, or (d) 0.4.
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