Decimal Fractions MCQs with Answers & Explanations (Page 5)

Factor 20 into a perfect square and another number, which is 4 * 5. Taking the square root of 4 gives 2, which leaves us with the simplified form 2*sqrt(5).

Begin by evaluating the left side: 832.58 - 242.31 = 590.27. Then arrange the right side calculation: x = 779.84 - 590.27 to pinpoint the correct missing value as 400.70.

Multiply both the top and the bottom by sqrt(5). This produces (5*sqrt(5)) / 5. Dividing by 5 leaves only the term sqrt(5).

Because both terms have sqrt(3), they are like radicals. Simply subtract the coefficients: 5 - 2 = 3, maintaining the radical to get 3*sqrt(3).

Raising to the 1/4 power means taking the fourth root. The number that multiplies by itself 4 times to equal 81 is 3 (3 * 3 * 3 * 3 = 81).

The fractional power 1/3 translates to the cube root. The cube root of 64 is 4, since 4^3 (or 4 * 4 * 4) equals 64.

Use the multiplication property of radicals to combine them into one root: sqrt(2 * 8) = sqrt(16). The square root of 16 perfectly evaluates to 4.

Separate x^3 into x^2 * x. Since x^2 is a perfect square, taking its square root gives x on the outside, leaving one x inside the radical: x*sqrt(x).

The target decimal is 2/5 = 0.4. Comparing absolute distances: |0.42 - 0.4| = 0.02, |0.40002 - 0.4| = 0.00002, and |0.400002 - 0.4| = 0.000002. Since 200001/500000 represents 0.400002, it presents the smallest deviation.

Convert 64 into a power of 4. We know that 4 * 4 * 4 equals 64, making it 4^3. Setting the exponents equal, we determine that x = 3.

Adding all the values while carrying over properly from the rightmost decimal places gives exactly 31.300.

To make calculation simpler, sum the values being subtracted: 13.829 + 7.302 + 1.214 = 22.345. Subtracting this from 58.621 produces 36.276.

To rewrite a term with a negative exponent, place it in the denominator with a positive exponent. Therefore, x^-2 is equivalent to 1/x^2.

Any non-zero number raised to the power of zero is always equal to 1. The negative sign is inside the parentheses, meaning the entire base of -5 is raised to the zero power, resulting in 1.

Calculating the individual values produces: (0.09)^2 = 0.0081, (1-0.9)^2 = (0.1)^2 = 0.01, and 1 - (0.9)^2 = 1 - 0.81 = 0.19. The number 0.0081 operates as the minimal absolute magnitude making it closest to zero.

Evaluate the numerical and variable parts separately. The square root of 16 is 4, and the square root of x^4 is x^2. This gives the exact simplified form 4x^2.

According to the zero exponent rule, any non-zero real number raised to the power of zero is always equal to 1. Therefore, 5^0 equals 1.

Using the quotient property, merge the terms into one square root: sqrt(50 / 2). This simplifies to sqrt(25), which has a value of 5.

Using the quotient rule, we keep the base of 3 and subtract the denominator's exponent from the numerator's exponent. The calculation 7 - 2 leaves us with 3^5.

Resolving the decimals first outputs 0.000001 (which amounts to exactly 10^-6). Multiplying 10^-6 and 10^7 combines the given exponents safely to construct a finalized value of 10.