Math / Numbers & Operations

QuestionWhich number is NOT an entire radical? $\sqrt[3]{343}$ $\sqrt{16}$ $\sqrt{35}$ $3 \sqrt{42}$

Studdy Solution

STEP 1

1. An entire radical is a radical expression that cannot be simplified further into a simpler radical form.
2. We need to determine which of the given numbers is not an entire radical.

STEP 2

1. Simplify each radical expression.
2. Identify the expression that is not an entire radical.

STEP 3

Simplify $\sqrt[3]{343}$ .
Since $343 = 7^3$ , we have:
$\sqrt[3]{343} = \sqrt[3]{7^3} = 7$

STEP 4

Simplify $\sqrt{16}$ .
Since $16 = 4^2$ , we have:
$\sqrt{16} = \sqrt{4^2} = 4$

STEP 5

Simplify $\sqrt{35}$ .
The number $35$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $5$ and $7$ .
$\sqrt{35} \text{ remains as } \sqrt{35}$

STEP 6

Simplify $3 \sqrt{42}$ .
The number $42$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $2$ , $3$ , and $7$ .
$3 \sqrt{42} \text{ remains as } 3 \sqrt{42}$

STEP 7

Identify the expression that is not an entire radical.
The expressions $\sqrt[3]{343}$ and $\sqrt{16}$ simplify to whole numbers $7$ and $4$ , respectively. The expressions $\sqrt{35}$ and $3 \sqrt{42}$ do not simplify to whole numbers, but $\sqrt{35}$ is a single radical expression that cannot be simplified further, making it an entire radical.
Therefore, the expression that is not an entire radical is:
$\boxed{3 \sqrt{42}}$

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QuestionWhich number is NOT an entire radical? $\sqrt[3]{343}$ $\sqrt{16}$ $\sqrt{35}$ $3 \sqrt{42}$

Studdy Solution

STEP 1

1. An entire radical is a radical expression that cannot be simplified further into a simpler radical form.
2. We need to determine which of the given numbers is not an entire radical.

STEP 2

1. Simplify each radical expression.
2. Identify the expression that is not an entire radical.

STEP 3

Simplify $\sqrt[3]{343}$ .
Since $343 = 7^3$ , we have:
$\sqrt[3]{343} = \sqrt[3]{7^3} = 7$

STEP 4

Simplify $\sqrt{16}$ .
Since $16 = 4^2$ , we have:
$\sqrt{16} = \sqrt{4^2} = 4$

STEP 5

Simplify $\sqrt{35}$ .
The number $35$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $5$ and $7$ .
$\sqrt{35} \text{ remains as } \sqrt{35}$

STEP 6

Simplify $3 \sqrt{42}$ .
The number $42$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $2$ , $3$ , and $7$ .
$3 \sqrt{42} \text{ remains as } 3 \sqrt{42}$

STEP 7

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QuestionWhich number is NOT an entire radical? 3433\sqrt[3]{343}3343​ 16\sqrt{16}16​ 35\sqrt{35}35​ 3423 \sqrt{42}342​

Studdy Solution

STEP 1

1. An entire radical is a radical expression that cannot be simplified further into a simpler radical form.2. We need to determine which of the given numbers is not an entire radical.

STEP 2

1. Simplify each radical expression.2. Identify the expression that is not an entire radical.

STEP 3

Simplify 3433\sqrt[3]{343}3343​.Since 343=73343 = 7^3343=73, we have:3433=733=7\sqrt[3]{343} = \sqrt[3]{7^3} = 73343​=373​=7

STEP 4

Simplify 16\sqrt{16}16​.Since 16=4216 = 4^216=42, we have:16=42=4\sqrt{16} = \sqrt{4^2} = 416​=42​=4

STEP 5

Simplify 35\sqrt{35}35​.The number 353535 is not a perfect square, and it cannot be simplified further because it is the product of prime numbers 555 and 777.35 remains as 35\sqrt{35} \text{ remains as } \sqrt{35}35​ remains as 35​

STEP 6

Simplify 3423 \sqrt{42}342​.The number 424242 is not a perfect square, and it cannot be simplified further because it is the product of prime numbers 222, 333, and 777.342 remains as 3423 \sqrt{42} \text{ remains as } 3 \sqrt{42}342​ remains as 342​

STEP 7

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QuestionWhich number is NOT an entire radical? $\sqrt[3]{343}$ $\sqrt{16}$ $\sqrt{35}$ $3 \sqrt{42}$

1. An entire radical is a radical expression that cannot be simplified further into a simpler radical form.
2. We need to determine which of the given numbers is not an entire radical.

1. Simplify each radical expression.
2. Identify the expression that is not an entire radical.

Simplify $\sqrt[3]{343}$ .
Since $343 = 7^3$ , we have:
$\sqrt[3]{343} = \sqrt[3]{7^3} = 7$

Simplify $\sqrt{16}$ .
Since $16 = 4^2$ , we have:
$\sqrt{16} = \sqrt{4^2} = 4$

Simplify $\sqrt{35}$ .
The number $35$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $5$ and $7$ .
$\sqrt{35} \text{ remains as } \sqrt{35}$

Simplify $3 \sqrt{42}$ .
The number $42$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $2$ , $3$ , and $7$ .
$3 \sqrt{42} \text{ remains as } 3 \sqrt{42}$