Math / Numbers & Operations

QuestionSimplify the following radical: $\sqrt{24}$
$4 \sqrt{6}$ $2 \sqrt{6}$

Studdy Solution

STEP 1

1. We are given the radical expression $\sqrt{24}$ to simplify.
2. We need to express $\sqrt{24}$ in its simplest radical form.

STEP 2

1. Factor the number under the radical.
2. Identify perfect squares.
3. Simplify the radical expression.

STEP 3

Factor the number $24$ under the radical.
$24 = 2 \times 12 = 2 \times 2 \times 6 = 2^3 \times 3$

STEP 4

Identify perfect squares among the factors of $24$ .
The perfect square is $2^2 = 4$ .

STEP 5

Rewrite $\sqrt{24}$ using the identified perfect square.
$\sqrt{24} = \sqrt{4 \times 6}$

STEP 6

Simplify the expression by taking the square root of the perfect square.
$\sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2 \times \sqrt{6}$
The simplified form of $\sqrt{24}$ is:
$\boxed{2 \sqrt{6}}$

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QuestionSimplify the following radical: $\sqrt{24}$
$4 \sqrt{6}$ $2 \sqrt{6}$

Studdy Solution

STEP 1

1. We are given the radical expression $\sqrt{24}$ to simplify.
2. We need to express $\sqrt{24}$ in its simplest radical form.

STEP 2

1. Factor the number under the radical.
2. Identify perfect squares.
3. Simplify the radical expression.

STEP 3

Factor the number $24$ under the radical.
$24 = 2 \times 12 = 2 \times 2 \times 6 = 2^3 \times 3$

STEP 4

Identify perfect squares among the factors of $24$ .
The perfect square is $2^2 = 4$ .

STEP 5

Rewrite $\sqrt{24}$ using the identified perfect square.
$\sqrt{24} = \sqrt{4 \times 6}$

STEP 6

Simplify the expression by taking the square root of the perfect square.
$\sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2 \times \sqrt{6}$
The simplified form of $\sqrt{24}$ is:
$\boxed{2 \sqrt{6}}$

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QuestionSimplify the following radical: 24\sqrt{24}24​464 \sqrt{6}46​ 262 \sqrt{6}26​

Studdy Solution

STEP 1

1. We are given the radical expression 24\sqrt{24}24​ to simplify.2. We need to express 24\sqrt{24}24​ in its simplest radical form.

STEP 2

1. Factor the number under the radical.2. Identify perfect squares.3. Simplify the radical expression.

STEP 3

Factor the number 242424 under the radical.24=2×12=2×2×6=23×3 24 = 2 \times 12 = 2 \times 2 \times 6 = 2^3 \times 3 24=2×12=2×2×6=23×3

STEP 4

Identify perfect squares among the factors of 242424.The perfect square is 22=42^2 = 422=4.

STEP 5

Rewrite 24\sqrt{24}24​ using the identified perfect square.24=4×6 \sqrt{24} = \sqrt{4 \times 6} 24​=4×6​

STEP 6

Simplify the expression by taking the square root of the perfect square.4×6=4×6=2×6 \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2 \times \sqrt{6} 4×6​=4​×6​=2×6​ The simplified form of 24\sqrt{24}24​ is:26\boxed{2 \sqrt{6}}26​​

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QuestionSimplify the following radical: $\sqrt{24}$
$4 \sqrt{6}$ $2 \sqrt{6}$

1. We are given the radical expression $\sqrt{24}$ to simplify.
2. We need to express $\sqrt{24}$ in its simplest radical form.

1. Factor the number under the radical.
2. Identify perfect squares.
3. Simplify the radical expression.

Factor the number $24$ under the radical.
$24 = 2 \times 12 = 2 \times 2 \times 6 = 2^3 \times 3$

Identify perfect squares among the factors of $24$ .
The perfect square is $2^2 = 4$ .

Rewrite $\sqrt{24}$ using the identified perfect square.
$\sqrt{24} = \sqrt{4 \times 6}$

Simplify the expression by taking the square root of the perfect square.
$\sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2 \times \sqrt{6}$
The simplified form of $\sqrt{24}$ is:
$\boxed{2 \sqrt{6}}$