Math Problem Statement
Solution
The image shows the mathematical expression .
To simplify this expression:
-
Combine the square roots:
-
Simplify (if possible). Since and have no common factors other than 1, the fraction is already in simplest form.
-
The expression simplifies to:
Alternatively, if you want to rationalize the denominator (expressing it without a square root in the denominator):
-
Multiply both the numerator and the denominator by :
-
Simplify . Since , we have:
-
The expression becomes:
Thus, .
Would you like further details or have any questions?
Here are 5 related questions to explore further:
- How do you rationalize a denominator with a square root?
- What are the steps for simplifying square roots of non-perfect squares?
- How can you express in simplest radical form?
- What are some methods to simplify complex fractions involving square roots?
- How do you multiply and simplify expressions involving square roots?
Tip: When simplifying square roots, always look for perfect square factors to simplify the radical expression.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Simplification of square roots
Rationalizing the denominator
Formulas
\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)
Rationalizing \(\frac{\sqrt{a}}{\sqrt{b}} = \frac{\sqrt{a} \cdot \sqrt{b}}{b}\)
Theorems
Properties of square roots
Suitable Grade Level
Grades 9-10