Find all the real square roots of 0.0004. A. 0.00632 and -0.00632 B. 0.06325 and -0.06325 C. 0.0002 and -0.0002 D. 0.02 and -0.02
The Correct Answer and Explanation is:
Correct Answer: D. 0.02 and -0.02
To find all the real square roots of 0.0004, we need to determine which number, when multiplied by itself, equals 0.0004. In mathematical terms, we are solving:x2=0.0004x^2 = 0.0004×2=0.0004
To find xxx, we take the square root of 0.0004. The square root of a number has two real roots when the number is positive: one positive and one negative. So we compute:0.0004=0.02\sqrt{0.0004} = 0.020.0004=0.02
Therefore, the two real square roots of 0.0004 are:x=0.02andx=−0.02x = 0.02 \quad \text{and} \quad x = -0.02x=0.02andx=−0.02
This is because:(0.02)2=0.02×0.02=0.0004(0.02)^2 = 0.02 \times 0.02 = 0.0004(0.02)2=0.02×0.02=0.0004(−0.02)2=(−0.02)×(−0.02)=0.0004(-0.02)^2 = (-0.02) \times (-0.02) = 0.0004(−0.02)2=(−0.02)×(−0.02)=0.0004
The other answer choices are incorrect for the following reasons:
- A. 0.00632 and -0.00632: (0.00632)2≈0.00003994(too small)(0.00632)^2 \approx 0.00003994 \quad \text{(too small)}(0.00632)2≈0.00003994(too small)
- B. 0.06325 and -0.06325: (0.06325)2≈0.004(too large)(0.06325)^2 \approx 0.004 \quad \text{(too large)}(0.06325)2≈0.004(too large)
- C. 0.0002 and -0.0002: (0.0002)2=0.00000004(much too small)(0.0002)^2 = 0.00000004 \quad \text{(much too small)}(0.0002)2=0.00000004(much too small)
- D. 0.02 and -0.02: (0.02)2=0.0004(correct)(0.02)^2 = 0.0004 \quad \text{(correct)}(0.02)2=0.0004(correct)
In conclusion, the correct answer is D, because both 0.02 and -0.02 satisfy the equation x2=0.0004x^2 = 0.0004×2=0.0004, and therefore are the real square roots of 0.0004.
