The number y is rational. Which statement about sqrt 35 + y is true? Choices: (A)sqrt 35 + y is rational. (B)sqrt 35 + y is irrational. (C)sqrt 35 + y can be rational or irrational, depending on the value of y.

Identify Type of Number: Identify whether sqrt(35) is a rational or irrational number. 35 is a non-perfect square, which means that sqrt(35) is an irrational number.Properties of Numbers: Understand the properties of rational and irrational numbers. Adding a rational number to an irrational number results in an irrational number. This is because the sum cannot be expressed as a ratio of two integers.Apply Property: Apply the property to the given problem. Since y is rational and sqrt(35) is irrational, the sum sqrt(35) + y will be irrational.

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The number $y$ is rational. Which statement about $\sqrt{35} + y$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{35} + y$ is rational. $\newline$ (B) $\sqrt{35} + y$ is irrational. $\newline$ (C) $\sqrt{35} + y$ can be rational or irrational, depending on the value of $y$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

y

is rational. Which statement about

\sqrt{35} + y

is true?

\newline

Choices:

\newline

(A)

\sqrt{35} + y

is rational.

\newline

(B)

\sqrt{35} + y

is irrational.

\newline

(C)

\sqrt{35} + y

can be rational or irrational, depending on the value of

y

Identify Type of Number: Identify whether $\sqrt{35}$ is a rational or irrational number. $35$ is a non-perfect square, which means that $\sqrt{35}$ is an irrational number.
Properties of Numbers: Understand the properties of rational and irrational numbers. Adding a rational number to an irrational number results in an irrational number. This is because the sum cannot be expressed as a ratio of two integers.
Apply Property: Apply the property to the given problem. $\newline$ Since $y$ is rational and $\sqrt{35}$ is irrational, the sum $\sqrt{35} + y$ will be irrational.