Question

Simplify each expression. $$\frac{\sqrt{2}}{3}+\frac{\sqrt{2}}{5}$$

   Simplify each expression.
$$\frac{\sqrt{2}}{3}+\frac{\sqrt{2}}{5}$$

Algebra for College Students

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 7, Problem 91

Instant Answer

Solved by Expert Ankit Gupta

07/01/2020

Step 1

The common denominator of 3 and 5 is 15. Show more…

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Simplify each expression. $$\frac{\sqrt{2}}{3}+\frac{\sqrt{2}}{5}$$

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Key Concepts

Common Denominator

A common denominator is a shared multiple of the denominators of two or more fractions, which is necessary when performing addition or subtraction. It simplifies the process by allowing the numerators to be combined directly after all fractions are rewritten with this common denominator.

Radical Expressions

Radical expressions involve roots, such as square roots, and following the rules for radicals is key in simplifying them. Like like terms, radicals with the same radicand can be combined by adding or subtracting their coefficients, similar to variables in algebra.

Fraction Addition with Radicals

When adding fractions that contain radical expressions in the numerator, both the process of finding a common denominator and combining like radicals are applied. This results in a simplified expression where the radical terms are combined after the fractions are expressed over a common denominator.

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