Math  /  Algebra

QuestionPoints: 00
Rationalize the denominator. Assume that all expressions under radicals represent 7x45\sqrt{\frac{7 x}{45}} 7x45=\sqrt{\frac{7 x}{45}}= \square

Studdy Solution
Simplify the expression:
- Simplify 45\sqrt{45} as 9×5=35\sqrt{9 \times 5} = 3\sqrt{5}. - Substitute back into the expression:
7x3545=335x45\frac{\sqrt{7x} \cdot 3\sqrt{5}}{45} = \frac{3\sqrt{35x}}{45}
- Simplify the fraction:
335x45=35x15\frac{3\sqrt{35x}}{45} = \frac{\sqrt{35x}}{15}
The rationalized expression is:
35x15\boxed{\frac{\sqrt{35x}}{15}}

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