Simplify the radical 5 x 4 45 \sqrt { \frac { 5 x ^ { 4 } } { 45 } } 45 5 x 4 .A) x 2 x ^ { 2 } x 2 B) x 2 3 \frac { x ^ { 2 } } { 3 } 3 x 2 C) x 3 \frac { x } { 3 } 3 x D) 1 3 \frac { 1 } { 3 } 3 1 E) x 2 5 x ^ { 2 } \sqrt { 5 } x 2 5

Question

Simplify the radical   5 x 4 45 \sqrt { \frac { 5 x ^ { 4 } } { 45 } } 45 5 x 4 ​ ​   .A)    x 2 x ^ { 2 } x 2 B)    x 2 3 \frac { x ^ { 2 } } { 3 } 3 x 2 ​ C)    x 3 \frac { x } { 3 } 3 x ​ D)    1 3 \frac { 1 } { 3 } 3 1 ​ E)    x 2 5 x ^ { 2 } \sqrt { 5 } x 2 5 ​

Mallory Katherine · Accepted Answer

Final Answer : B, Explanation :   5 x 4 45 = 1 9 ⋅ 5 ( x 2 ) 2 5 = x 2 3 1 5 = x 2 3 ⋅ 5 5 = x 2 5 3 \sqrt{\frac{5x^4}{45}} = \sqrt{\frac{1}{9} \cdot \frac{5(x^2)^2}{5}} = \frac{x^2}{3} \sqrt{\frac{1}{5}} = \frac{x^2}{3} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{x^2\sqrt{5}}{3} 45 5 x 4 ​ ​ = 9 1 ​ ⋅ 5 5 ( x 2 ) 2 ​ ​ = 3 x 2 ​ 5 1 ​ ​ = 3 x 2 ​ ⋅ 5 ​ 5 ​ ​ = 3 x 2 5 ​ ​   So the answer is $\boxed{	extbf{(B)}}$.

Simplify the radical $5x445\sqrt { \frac { 5 x ^ { 4 } } { 45 } }$ .

A) $x ^ { 2 }$
B) $x23\frac { x ^ { 2 } } { 3 }$
C) $x3\frac { x } { 3 }$

D) $13\frac { 1 } { 3 }$
E) $\sqrt { 5 }$

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Learning Objectives

Learning Objectives

Related questions

Simplify the radical 5x445\sqrt { \frac { 5 x ^ { 4 } } { 45 } }455x4​​ .A) x2x ^ { 2 }x2 B) x23\frac { x ^ { 2 } } { 3 }3x2​ C) x3\frac { x } { 3 }3x​ D) 13\frac { 1 } { 3 }31​ E) x25x ^ { 2 } \sqrt { 5 }x25​

Definitions

Learning Objectives

Learning Objectives

Related questions

Simplify the radical $5x445\sqrt { \frac { 5 x ^ { 4 } } { 45 } }$ .

A) $x ^ { 2 }$
B) $x23\frac { x ^ { 2 } } { 3 }$
C) $x3\frac { x } { 3 }$

D) $13\frac { 1 } { 3 }$
E) $\sqrt { 5 }$