Decimal Fractions MCQs with Answers & Explanations (Page 8)

Multiply the numbers inside the roots to get sqrt(100). The principal square root of 100 is 10, completing the simplification.

To isolate x, perform the inverse operation of a square root by squaring both sides of the equation. Squaring 5 gives 25, so x = 25.

Applying the exponent rule for division, subtract the exponent 4 from the exponent 6 while maintaining the base of 5. This results in 5^2.

Raising a number to the power of 1/3 is the same as finding its cube root. The cube root of 8 is 2, because 2^3 = 8.

Subtracting the exponents 8 - 7 gives 1. Any variable raised to the power of 1 is just the variable itself, so a^1 is written simply as a.

Multiplying a square root by itself cancels out the radical, effectively squaring the square root. sqrt(6) * sqrt(6) is sqrt(36), which immediately simplifies to 6.

The bounds are 3/4 = 0.75 and 5/6 ≈ 0.833. Analyzing the options: 1/2 = 0.50, 2/3 ≈ 0.667, 4/5 = 0.80, and 9/10 = 0.90. The only fraction falling within the 0.75 to 0.833 range is 4/5.

Multiply numerator and denominator by sqrt(3) to rationalize. This gives (3*sqrt(3)) / 3. The 3s cancel out, leaving just sqrt(3).

The boundaries correspond to roughly 0.333 and 0.875. Evaluating the options gives: 1/4 = 0.25, 23/24 ≈ 0.958, 11/12 ≈ 0.917, and 17/24 ≈ 0.708. Only 17/24 sits correctly within this boundary.

There are 3600 seconds in one hour (60 minutes × 60 seconds). Therefore, one second is 1/3600 of an hour, which mathematically evaluates to approximately 0.000277... or rounded to 0.00027.

To remove the cube root, cube both sides of the equation. The cube of 3 is 3 * 3 * 3, which equals 27. Therefore, x = 27.

Look for a perfect cube factor of 16, which is 8. Writing cbrt(16) as cbrt(8 * 2) allows us to bring out the cube root of 8 (which is 2), yielding 2*cbrt(2).

The largest perfect square that divides 27 is 9. We can write sqrt(27) as sqrt(9 * 3). The square root of 9 is 3, making the simplified form 3*sqrt(3).

The valid interval boundaries are 7/13 (≈ 0.538) and 4/5 (0.80). Checking the values: 1/2 = 0.5 (falls below 0.538), 2/3 ≈ 0.667, 3/4 = 0.75, 5/7 ≈ 0.714. Hence, 1/2 does not belong inside the targeted range.

A negative exponent means taking the reciprocal of the base and making the exponent positive. So, 2^-3 becomes 1/(2^3), which evaluates to 1/8.

Step-by-step solution: 1. Align the decimal points for both numbers. 2. Add 7.3 + 0.68 = 7.98. 3. Ensure the result is rounded to three decimal places.

Step-by-step solution: 1. Ignore the decimal points and multiply as whole numbers. 2. Count the total decimal places (three) and place the decimal accordingly. 3. The product is 0.546.

Step-by-step solution: 1. Align the decimal points for both numbers. 2. Add 8.1 + 0.76 = 8.86. 3. Ensure the result is rounded to three decimal places.

Step-by-step solution: 1. Align the decimal points for both numbers. 2. Add 8.3 + 0.78 = 9.08. 3. Ensure the result is rounded to three decimal places.

Step-by-step solution: 1. Align the decimal points for both numbers. 2. Add 10.7 + 1.02 = 11.72. 3. Ensure the result is rounded to three decimal places.