Number

To simplify a surd, we find the largest square factor of 48, which is 16, giving the square root of 16 times 3, or 4 times the square root of 3. Option D is incorrect because it is not fully simplified, as the square root of 12 still contains a square factor of 4. Option A is incorrect because it simplifies to the square root of 32 instead of 48.

Rounding each number to one significant figure gives 30 times 4 divided by 2, which simplifies to 120 divided by 2, resulting in an estimate of 60. Option D is incorrect because it represents only the numerator's estimate of 120, forgetting to divide by 2. Option A is too low and likely results from incorrect rounding or division.

To write 0.000045 in standard scientific notation, the decimal point must be moved five places to the right to obtain a coefficient between 1 and 10, which yields 4.5 multiplied by 10 to the power of negative 5. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option C is incorrect because 45 is not between 1 and 10.
• !Option D is incorrect because it is not fully simplified, as the square root of 12 still contains a square factor of 4.
• !Option D is incorrect because it represents only the numerator's estimate of 120, forgetting to divide by 2.

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