QuestionIdentify the irrational numbers from the following: a. $\sqrt{53}$ , b. $\sqrt{49}$ , c. $\sqrt{256}$ , d. $\sqrt{245}$ , e. $2-3 \sqrt{3}$ , f. $\sqrt{3} \cdot 5$ . Choose all that apply.

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a number is irrational if the number is not a perfect square.

STEP 2

We can determine if a number is irrational by taking its square root. If the square root is not a whole number, then the original number is irrational.

STEP 3

Calculate the square root of53.
$\sqrt{53}$

STEP 4

Since53 is not a perfect square, its square root is not a whole number and therefore it is irrational.

STEP 5

Calculate the square root of49.
$\sqrt{49}$

STEP 6

Since49 is a perfect square (^2), its square root is a whole number () and therefore it is not irrational.

STEP 7

Calculate the square root of256.
$\sqrt{256}$

STEP 8

Since256 is a perfect square (16^2), its square root is a whole number (16) and therefore it is not irrational.

STEP 9

Calculate the square root of245.
$\sqrt{245}$

STEP 10

Since245 is not a perfect square, its square root is not a whole number and therefore it is irrational.

STEP 11

For the expression $-3 \sqrt{3}$ , we know that $\sqrt{3}$ is irrational. Therefore, any operation involving an irrational number and a rational number (in this case, multiplication by -3 and addition of) will result in an irrational number.

STEP 12

For the expression $\sqrt{} \cdot5$ , we know that $\sqrt{}$ is irrational. Therefore, any operation involving an irrational number and a rational number (in this case, multiplication by5) will result in an irrational number.
The irrational numbers from the given options are $\sqrt{53}$ , $\sqrt{245}$ , $2- \sqrt{}$ , and $\sqrt{} \cdot5$ . So, the correct options are B, D, F, and C.

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QuestionIdentify the irrational numbers from the following: a. $\sqrt{53}$ , b. $\sqrt{49}$ , c. $\sqrt{256}$ , d. $\sqrt{245}$ , e. $2-3 \sqrt{3}$ , f. $\sqrt{3} \cdot 5$ . Choose all that apply.

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a number is irrational if the number is not a perfect square.

STEP 2

We can determine if a number is irrational by taking its square root. If the square root is not a whole number, then the original number is irrational.

STEP 3

Calculate the square root of53.
$\sqrt{53}$

STEP 4

Since53 is not a perfect square, its square root is not a whole number and therefore it is irrational.

STEP 5

Calculate the square root of49.
$\sqrt{49}$

STEP 6

Since49 is a perfect square (^2), its square root is a whole number () and therefore it is not irrational.

STEP 7

Calculate the square root of256.
$\sqrt{256}$

STEP 8

Since256 is a perfect square (16^2), its square root is a whole number (16) and therefore it is not irrational.

STEP 9

Calculate the square root of245.
$\sqrt{245}$

STEP 10

Since245 is not a perfect square, its square root is not a whole number and therefore it is irrational.

STEP 11

For the expression $-3 \sqrt{3}$ , we know that $\sqrt{3}$ is irrational. Therefore, any operation involving an irrational number and a rational number (in this case, multiplication by -3 and addition of) will result in an irrational number.

STEP 12

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QuestionIdentify the irrational numbers from the following: a. 53\sqrt{53}53​, b. 49\sqrt{49}49​, c. 256\sqrt{256}256​, d. 245\sqrt{245}245​, e. 2−332-3 \sqrt{3}2−33​, f. 3⋅5\sqrt{3} \cdot 53​⋅5. Choose all that apply.

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a number is irrational if the number is not a perfect square.

STEP 2

We can determine if a number is irrational by taking its square root. If the square root is not a whole number, then the original number is irrational.

STEP 3

Calculate the square root of53.53\sqrt{53}53​

STEP 4

Since53 is not a perfect square, its square root is not a whole number and therefore it is irrational.

STEP 5

Calculate the square root of49.49\sqrt{49}49​

STEP 6

Since49 is a perfect square (^2), its square root is a whole number () and therefore it is not irrational.

STEP 7

Calculate the square root of256.256\sqrt{256}256​

STEP 8

Since256 is a perfect square (16^2), its square root is a whole number (16) and therefore it is not irrational.

STEP 9

Calculate the square root of245.245\sqrt{245}245​

STEP 10

Since245 is not a perfect square, its square root is not a whole number and therefore it is irrational.

STEP 11

For the expression −33-3 \sqrt{3}−33​, we know that 3\sqrt{3}3​ is irrational. Therefore, any operation involving an irrational number and a rational number (in this case, multiplication by -3 and addition of) will result in an irrational number.

STEP 12

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

QuestionIdentify the irrational numbers from the following: a. $\sqrt{53}$ , b. $\sqrt{49}$ , c. $\sqrt{256}$ , d. $\sqrt{245}$ , e. $2-3 \sqrt{3}$ , f. $\sqrt{3} \cdot 5$ . Choose all that apply.

Calculate the square root of53.
$\sqrt{53}$

Calculate the square root of49.
$\sqrt{49}$

Calculate the square root of256.
$\sqrt{256}$

Calculate the square root of245.
$\sqrt{245}$

For the expression $-3 \sqrt{3}$ , we know that $\sqrt{3}$ is irrational. Therefore, any operation involving an irrational number and a rational number (in this case, multiplication by -3 and addition of) will result in an irrational number.