QuestionFind the product of $\sqrt{23}$ and $2 \sqrt{23}$ , and state if the result is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the product of $\sqrt{23}$ and $\sqrt{23}$ . . We are also asked to determine whether the result is rational or irrational.

STEP 2

First, we need to calculate the product of $\sqrt{23}$ and $2 \sqrt{23}$ . We can do this by multiplying the two expressions together.
$Product = \sqrt{23} \times2 \sqrt{23}$

STEP 3

Next, we realize that the multiplication of two square roots is the square root of their multiplication. Also, the multiplication of two identical square roots is the number under the root. So, we can simplify the expression as follows $Product =2 \times \sqrt{23} \times \sqrt{23} =2 \times23$

STEP 4

Now, calculate the product.
$Product =2 \times23 =46$

STEP 5

The product of $\sqrt{23}$ and $2 \sqrt{23}$ is46.

STEP 6

Now, we need to determine whether the result is rational or irrational. A rational number can be expressed as a fraction where both the numerator and the denominator are integers (and the denominator is not zero). Since46 can be expressed as a fraction where the numerator is46 and the denominator is1, it is a rational number.
The product of $\sqrt{23}$ and $2 \sqrt{23}$ is a rational number.

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QuestionFind the product of $\sqrt{23}$ and $2 \sqrt{23}$ , and state if the result is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the product of $\sqrt{23}$ and $\sqrt{23}$ . . We are also asked to determine whether the result is rational or irrational.

STEP 2

First, we need to calculate the product of $\sqrt{23}$ and $2 \sqrt{23}$ . We can do this by multiplying the two expressions together.
$Product = \sqrt{23} \times2 \sqrt{23}$

STEP 3

Next, we realize that the multiplication of two square roots is the square root of their multiplication. Also, the multiplication of two identical square roots is the number under the root. So, we can simplify the expression as follows $Product =2 \times \sqrt{23} \times \sqrt{23} =2 \times23$

STEP 4

Now, calculate the product.
$Product =2 \times23 =46$

STEP 5

The product of $\sqrt{23}$ and $2 \sqrt{23}$ is46.

STEP 6

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QuestionFind the product of 23\sqrt{23}23​ and 2232 \sqrt{23}223​, and state if the result is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the product of 23\sqrt{23}23​ and 23 \sqrt{23}23​. . We are also asked to determine whether the result is rational or irrational.

STEP 2

First, we need to calculate the product of 23\sqrt{23}23​ and 2232 \sqrt{23}223​. We can do this by multiplying the two expressions together.Product=23×223Product = \sqrt{23} \times2 \sqrt{23}Product=23​×223​

STEP 3

STEP 4

Now, calculate the product.Product=2×23=46Product =2 \times23 =46Product=2×23=46

STEP 5

The product of 23\sqrt{23}23​ and 2232 \sqrt{23}223​ is46.

STEP 6

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the product of $\sqrt{23}$ and $2 \sqrt{23}$ , and state if the result is rational or irrational.

Assumptions1. We are asked to find the product of $\sqrt{23}$ and $\sqrt{23}$ . . We are also asked to determine whether the result is rational or irrational.

First, we need to calculate the product of $\sqrt{23}$ and $2 \sqrt{23}$ . We can do this by multiplying the two expressions together.
$Product = \sqrt{23} \times2 \sqrt{23}$

Now, calculate the product.
$Product =2 \times23 =46$

The product of $\sqrt{23}$ and $2 \sqrt{23}$ is46.