Final answer:
To find an equivalent expression, apply the properties of exponents and radicals. After simplifying both √8x2 and √3x, and then performing the division, the result is √8x/3.
Step-by-step explanation:
To find an expression equivalent to the quotient √8x2 + √3x, we need to apply the properties of radicals and exponents. Recall from Eq. A.8 as a reference that when multiplying numbers with the same base, we add the exponents, and this property also applies to radicals. A radicand with an exponent can be expressed as a fractional exponent, such that x2 = √x.
By this logic, √8x2 can be rewritten as (8x2)1/2, and √3x is (3x)1/2. But the question refers to a quotient of these expressions, which suggests division. Applying the rule for dividing powers with the same base (“am/an = am-n”) we can subtract the exponents.
√8x2 can actually be simplified to 2x√2 where 2x is under the radical due to the square root of x2, and √2 is the simplified radical form of 8. When we divide 2x√2 by √3x, the x under the root will cancel out, leaving us with the simplified form of √2x/3. Therefore, the equivalent expression is option (d) √8x/3.