Math Problem Statement

√ 3\5

Solution

It looks like you're asking to simplify or express the value of 35\sqrt{\frac{3}{5}}.

Simplified form:

35=35\sqrt{\frac{3}{5}} = \frac{\sqrt{3}}{\sqrt{5}} This is the exact form.

Approximate decimal value:

To get a decimal approximation: 31.732and52.236\sqrt{3} \approx 1.732 \quad \text{and} \quad \sqrt{5} \approx 2.236 Thus, 351.7322.2360.774\frac{\sqrt{3}}{\sqrt{5}} \approx \frac{1.732}{2.236} \approx 0.774

So, 350.774\sqrt{\frac{3}{5}} \approx 0.774 (rounded to three decimal places).

Would you like further details on how to rationalize the denominator or have any other questions?

Here are some related questions for practice:

  1. Simplify 47\sqrt{\frac{4}{7}}.
  2. Find the decimal approximation of 2\sqrt{2}.
  3. Simplify 82\frac{\sqrt{8}}{\sqrt{2}}.
  4. Solve 126\frac{\sqrt{12}}{\sqrt{6}}.
  5. Approximate 57\frac{\sqrt{5}}{\sqrt{7}}.

Tip: To rationalize a square root in a denominator, multiply both the numerator and denominator by the same square root to remove it.

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Math Problem Analysis

Mathematical Concepts

Radicals
Simplification
Decimal Approximation

Formulas

√(a/b) = √a / √b
Approximation of square roots

Theorems

Properties of square roots
Rationalizing the denominator

Suitable Grade Level

Grades 7-9