Asked by Filip Gabric on Jun 10, 2024
Verified
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
Simplify
Making an algebraic expression easier to understand by combining like terms or applying mathematical operations.
Radical
A mathematical symbol (√) used to denote the square root or nth root of a number or expression.
Expression
A combination of symbols that represents a mathematical concept or quantity.
- Streamline variable-containing radical expressions.
Verified Answer
MK
Mallory KatherineJun 11, 2024
Final Answer :
B
Explanation :
5x445=19⋅5(x2)25=x2315=x23⋅55=x253\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}455x4=91⋅55(x2)2=3x251=3x2⋅55=3x25 So the answer is $\boxed{\textbf{(B)}}$.
Learning Objectives
- Streamline variable-containing radical expressions.