Math Problem Statement

5\sqrt2 $$$$ $$$$ +2\sqrt{\frac72}

Solution

To simplify the expression 52+2725\sqrt{2} + 2\sqrt{\frac{7}{2}}, let's break down each term and simplify if possible.

  1. Simplify each term:

    • The term 525\sqrt{2} is already in its simplest form.
    • For the term 2722\sqrt{\frac{7}{2}}, we can simplify it further:

    272=2×722\sqrt{\frac{7}{2}} = 2 \times \frac{\sqrt{7}}{\sqrt{2}}

  2. Simplify the fraction under the square root:

    2×72=2×72×22=2×142=142 \times \frac{\sqrt{7}}{\sqrt{2}} = 2 \times \frac{\sqrt{7}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2 \times \frac{\sqrt{14}}{2} = \sqrt{14}

    Now, the expression simplifies to:

    52+145\sqrt{2} + \sqrt{14}

  3. Conclusion:

    The expression 52+2725\sqrt{2} + 2\sqrt{\frac{7}{2}} simplifies to:

    52+14\boxed{5\sqrt{2} + \sqrt{14}}

This is the simplest form of the given expression.

Would you like more details or have any questions?

Here are 5 related questions to further explore the topic:

  1. How do you simplify expressions involving square roots of fractions?
  2. What are some common rules for simplifying square root expressions?
  3. Can you explain the concept of like and unlike terms in expressions involving square roots?
  4. How can you rationalize a denominator involving a square root?
  5. What are some practical applications of simplifying square root expressions in real-life problems?

Tip: When simplifying square root expressions, look for opportunities to factor out squares or simplify fractions under the square root to make the expression easier to handle.

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Math Problem Analysis

Mathematical Concepts

Simplifying expressions
Square roots
Fractional exponents

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12