Math Problem Statement

Rationalize the denominator of \( \frac{9}{\sqrt{3}} \).

Solution

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Question 7, 17.5.15:
"Rationalize the denominator of 93\frac{9}{\sqrt{3}}."

The task seems to be asking you to rationalize the denominator of the given expression.

Solution:

To rationalize 93\frac{9}{\sqrt{3}}, we need to eliminate the square root from the denominator. We do this by multiplying both the numerator and the denominator by 3\sqrt{3}:

93×33=933\frac{9}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{9\sqrt{3}}{3}

Now, simplify the expression:

933=33\frac{9\sqrt{3}}{3} = 3\sqrt{3}

So, the rationalized form of 93\frac{9}{\sqrt{3}} is 333\sqrt{3}.

Would you like more details on how to rationalize denominators or have any further questions about this problem?

Related Questions:

  1. How do you rationalize denominators when there is a binomial expression in the denominator?
  2. What is the significance of rationalizing denominators in mathematics?
  3. Can you explain the process of simplifying radical expressions with square roots?
  4. What happens when you rationalize the denominator of 57\frac{5}{\sqrt{7}}?
  5. How would you rationalize 62+3\frac{6}{\sqrt{2} + \sqrt{3}}?

Tip: Always multiply both the numerator and denominator by the conjugate of the denominator when you have a binomial expression with square roots.

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Math Problem Analysis

Mathematical Concepts

Simplifying Radicals
Rationalizing Denominators

Formulas

\( \frac{a}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} = \frac{a\sqrt{b}}{b} \)

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 8-10