Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The number vv is rational. Which statement about 38v\sqrt{38} - v is true?\newlineChoices:\newline(A) 38v\sqrt{38} - v is rational.\newline(B) 38v\sqrt{38} - v is irrational.\newline(C) 38v\sqrt{38} - v can be rational or irrational, depending on the value of vv.

Full solution

Q. The number vv is rational. Which statement about 38v\sqrt{38} - v is true?\newlineChoices:\newline(A) 38v\sqrt{38} - v is rational.\newline(B) 38v\sqrt{38} - v is irrational.\newline(C) 38v\sqrt{38} - v can be rational or irrational, depending on the value of vv.
  1. Identify Type of Number: Identify whether 38\sqrt{38} is a rational or irrational number. 3838 is a non-perfect square, which means that 38\sqrt{38} is an irrational number.
  2. Consider Number Properties: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.
  3. Apply Property to Problem: Apply the property to the given problem.\newlineSince vv is rational and 38\sqrt{38} is irrational, 38v\sqrt{38} - v will always be irrational.

More problems from Properties of operations on rational and irrational numbers