Math / Algebra

Question3) $\sqrt{512 k^{2}}$

Studdy Solution

STEP 1

1. We are asked to simplify the expression $\sqrt{512 k^{2}}$ .
2. The expression involves a square root of a product, which can be simplified by separating the square root of each factor.

STEP 2

1. Simplify the square root of the numerical factor 512.
2. Simplify the square root of the variable factor $k^2$ .
3. Combine the simplified results.

STEP 3

Simplify the square root of 512. First, factor 512 into its prime factors:
$512 = 2^9$
Since 512 is a power of 2, we can simplify the square root:
$\sqrt{512} = \sqrt{2^9} = 2^{9/2} = 2^{4.5} = 2^4 \times \sqrt{2} = 16\sqrt{2}$

STEP 4

Simplify the square root of $k^2$ :
$\sqrt{k^2} = k$
Assuming $k$ is non-negative, as we are dealing with real numbers.

STEP 5

Combine the results from the previous steps:
$\sqrt{512 k^2} = \sqrt{512} \times \sqrt{k^2} = 16\sqrt{2} \times k = 16k\sqrt{2}$
The simplified expression is:
$\boxed{16k\sqrt{2}}$

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Question3) $\sqrt{512 k^{2}}$

Studdy Solution

STEP 1

1. We are asked to simplify the expression $\sqrt{512 k^{2}}$ .
2. The expression involves a square root of a product, which can be simplified by separating the square root of each factor.

STEP 2

1. Simplify the square root of the numerical factor 512.
2. Simplify the square root of the variable factor $k^2$ .
3. Combine the simplified results.

STEP 3

Simplify the square root of 512. First, factor 512 into its prime factors:
$512 = 2^9$
Since 512 is a power of 2, we can simplify the square root:
$\sqrt{512} = \sqrt{2^9} = 2^{9/2} = 2^{4.5} = 2^4 \times \sqrt{2} = 16\sqrt{2}$

STEP 4

Simplify the square root of $k^2$ :
$\sqrt{k^2} = k$
Assuming $k$ is non-negative, as we are dealing with real numbers.

STEP 5

Combine the results from the previous steps:
$\sqrt{512 k^2} = \sqrt{512} \times \sqrt{k^2} = 16\sqrt{2} \times k = 16k\sqrt{2}$
The simplified expression is:
$\boxed{16k\sqrt{2}}$

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Question3) 512k2\sqrt{512 k^{2}}512k2​

Studdy Solution

STEP 1

1. We are asked to simplify the expression 512k2\sqrt{512 k^{2}}512k2​.2. The expression involves a square root of a product, which can be simplified by separating the square root of each factor.

STEP 2

1. Simplify the square root of the numerical factor 512.2. Simplify the square root of the variable factor k2k^2k2.3. Combine the simplified results.

STEP 3

STEP 4

Simplify the square root of k2k^2k2:k2=k \sqrt{k^2} = k k2​=kAssuming kkk is non-negative, as we are dealing with real numbers.

STEP 5

Combine the results from the previous steps:512k2=512×k2=162×k=16k2 \sqrt{512 k^2} = \sqrt{512} \times \sqrt{k^2} = 16\sqrt{2} \times k = 16k\sqrt{2} 512k2​=512​×k2​=162​×k=16k2​The simplified expression is:16k2 \boxed{16k\sqrt{2}} 16k2​​

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Question3) $\sqrt{512 k^{2}}$

1. We are asked to simplify the expression $\sqrt{512 k^{2}}$ .
2. The expression involves a square root of a product, which can be simplified by separating the square root of each factor.

1. Simplify the square root of the numerical factor 512.
2. Simplify the square root of the variable factor $k^2$ .
3. Combine the simplified results.

Simplify the square root of $k^2$ :
$\sqrt{k^2} = k$
Assuming $k$ is non-negative, as we are dealing with real numbers.

Combine the results from the previous steps:
$\sqrt{512 k^2} = \sqrt{512} \times \sqrt{k^2} = 16\sqrt{2} \times k = 16k\sqrt{2}$
The simplified expression is:
$\boxed{16k\sqrt{2}}$