Question

When the equation 35% =v√355 is evaluated for x, you derive an equivalent form of the radical 355 in rational exponent form: 35%. What is the value of x?

A) x = 5

B) x = 7

C) x = 5/7

D) x = 7/5

Answer 1

The square root of 355 can be expressed as 355 to the power of ⅛. By equating this with 35% (0.35) and solving for x, the value of x is found to be 7/5, corresponding to option D.

Step-by-step explanation:

The equation 35% = v∙355 needs to be evaluated for x to derive the equivalent radical in rational exponent form. This expression can be rewritten using the properties of exponents. If we interpret x as the square root of x, we get x² = ∙x. Using this rule, we convert the square root of a number to a fractional exponent by expressing the radical as x to the power of ⅛ (1/2).

Therefore, we can re-express the square root of 355 as 355⅛. Since 35% represents 0.35 in decimal form, our equation becomes 0.35 = 355⅛. To find the value of x, we simply raise both sides of the equation to the power of 2 (which is the reciprocal of ⅛) to get x on its own:

• (0.35)² = (355⅛)²
• x = 355²
• x = 7/5

Hence, after performing the calculations, we conclude that the value of x is 7/5, which corresponds to option D.