Math / Algebra

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Radicals Simplifying a radical expression with an odd exponent
Simplify. $\sqrt{16 u^{9}}$
Assume that the variable represents a positive real number.

Studdy Solution

STEP 1

1. The expression to simplify is $\sqrt{16 u^{9}}$ .
2. The variable $u$ represents a positive real number.
3. Simplifying involves expressing the radical in terms of integer exponents.

STEP 2

1. Simplify the numerical part of the radical.
2. Simplify the variable part of the radical.

STEP 3

Simplify the numerical part of the radical $\sqrt{16}$ .
$\sqrt{16} = 4$

STEP 4

Simplify the variable part of the radical $\sqrt{u^9}$ .
First, express $u^9$ as a power suitable for simplification:
$u^9 = (u^4)^2 \times u$
This allows us to use the property of radicals $\sqrt{a^2} = a$ .

STEP 5

Apply the property of radicals to simplify $\sqrt{(u^4)^2 \times u}$ :
$\sqrt{(u^4)^2 \times u} = u^4 \times \sqrt{u}$

STEP 6

Combine the simplified numerical and variable parts:
$\sqrt{16 u^9} = 4 \times u^4 \times \sqrt{u}$
The simplified expression is:
$\boxed{4u^4\sqrt{u}}$

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Questionwy Apps
Radicals Simplifying a radical expression with an odd exponent
Simplify. $\sqrt{16 u^{9}}$
Assume that the variable represents a positive real number.

Studdy Solution

STEP 1

1. The expression to simplify is $\sqrt{16 u^{9}}$ .
2. The variable $u$ represents a positive real number.
3. Simplifying involves expressing the radical in terms of integer exponents.

STEP 2

1. Simplify the numerical part of the radical.
2. Simplify the variable part of the radical.

STEP 3

Simplify the numerical part of the radical $\sqrt{16}$ .
$\sqrt{16} = 4$

STEP 4

Simplify the variable part of the radical $\sqrt{u^9}$ .
First, express $u^9$ as a power suitable for simplification:
$u^9 = (u^4)^2 \times u$
This allows us to use the property of radicals $\sqrt{a^2} = a$ .

STEP 5

Apply the property of radicals to simplify $\sqrt{(u^4)^2 \times u}$ :
$\sqrt{(u^4)^2 \times u} = u^4 \times \sqrt{u}$

STEP 6

Combine the simplified numerical and variable parts:
$\sqrt{16 u^9} = 4 \times u^4 \times \sqrt{u}$
The simplified expression is:
$\boxed{4u^4\sqrt{u}}$

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Questionwy AppsRadicals Simplifying a radical expression with an odd exponentSimplify. 16u9\sqrt{16 u^{9}}16u9​Assume that the variable represents a positive real number.

Studdy Solution

STEP 1

1. The expression to simplify is 16u9\sqrt{16 u^{9}}16u9​.2. The variable uuu represents a positive real number.3. Simplifying involves expressing the radical in terms of integer exponents.

STEP 2

1. Simplify the numerical part of the radical.2. Simplify the variable part of the radical.

STEP 3

Simplify the numerical part of the radical 16\sqrt{16}16​.16=4 \sqrt{16} = 4 16​=4

STEP 4

Simplify the variable part of the radical u9\sqrt{u^9}u9​.First, express u9u^9u9 as a power suitable for simplification:u9=(u4)2×u u^9 = (u^4)^2 \times u u9=(u4)2×uThis allows us to use the property of radicals a2=a\sqrt{a^2} = aa2​=a.

STEP 5

Apply the property of radicals to simplify (u4)2×u\sqrt{(u^4)^2 \times u}(u4)2×u​:(u4)2×u=u4×u \sqrt{(u^4)^2 \times u} = u^4 \times \sqrt{u} (u4)2×u​=u4×u​

STEP 6

Combine the simplified numerical and variable parts:16u9=4×u4×u \sqrt{16 u^9} = 4 \times u^4 \times \sqrt{u} 16u9​=4×u4×u​ The simplified expression is:4u4u \boxed{4u^4\sqrt{u}} 4u4u​​

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Questionwy Apps
Radicals Simplifying a radical expression with an odd exponent
Simplify. $\sqrt{16 u^{9}}$
Assume that the variable represents a positive real number.

1. The expression to simplify is $\sqrt{16 u^{9}}$ .
2. The variable $u$ represents a positive real number.
3. Simplifying involves expressing the radical in terms of integer exponents.

1. Simplify the numerical part of the radical.
2. Simplify the variable part of the radical.

Simplify the numerical part of the radical $\sqrt{16}$ .
$\sqrt{16} = 4$

Simplify the variable part of the radical $\sqrt{u^9}$ .
First, express $u^9$ as a power suitable for simplification:
$u^9 = (u^4)^2 \times u$
This allows us to use the property of radicals $\sqrt{a^2} = a$ .

Apply the property of radicals to simplify $\sqrt{(u^4)^2 \times u}$ :
$\sqrt{(u^4)^2 \times u} = u^4 \times \sqrt{u}$

Combine the simplified numerical and variable parts:
$\sqrt{16 u^9} = 4 \times u^4 \times \sqrt{u}$
The simplified expression is:
$\boxed{4u^4\sqrt{u}}$