Math Problem Statement

1/root 5

Solution

The expression 15\frac{1}{\sqrt{5}} can be simplified or written in a more useful form. If you'd like to calculate it, here's the approximation:

150.4472\frac{1}{\sqrt{5}} \approx 0.4472

If you'd like to rationalize the denominator (eliminate the square root from the denominator), you can multiply both the numerator and denominator by 5\sqrt{5}:

15=1×55×5=55\frac{1}{\sqrt{5}} = \frac{1 \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{5}}{5}

So, the exact simplified form is:

55\frac{\sqrt{5}}{5}

Would you like more details or have any questions about this?

Here are 5 related questions:

  1. What is the decimal approximation of 5\sqrt{5}?
  2. How can you rationalize a denominator in a general case?
  3. What is the value of 12\frac{1}{\sqrt{2}}?
  4. How do you find the square root of non-perfect squares like 5?
  5. What is the significance of rationalizing a denominator?

Tip: Rationalizing denominators is often done to simplify expressions, especially when dealing with irrational numbers.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots
Rationalization

Formulas

\( \frac{1}{\sqrt{5}} \)
\( \frac{\sqrt{5}}{5} \)

Theorems

Rationalizing the Denominator

Suitable Grade Level

Grades 7-9