Algebra

sqrt(1/5) + sqrt(4/5) + sqrt(5/4)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Simplify each square root separately

We have three terms to simplify. We'll handle each one on its own before adding them together.
2

Simplify the first term

We split the square root into numerator and denominator. Then we rationalize by multiplying top and bottom by .
3

Simplify the second term

Same process: split, simplify , then rationalize the denominator.
4

Simplify the third term

Here the denominator is a perfect square, so no rationalization is needed. and we're done.
5

Find a common denominator for all terms

The denominators are 5, 5, and 2. The least common denominator (LCD) is 10.
6

Rewrite each fraction with denominator 10

Multiply the first two fractions by and the third by to get a common denominator of 10.
7

Add the fractions together

Since all terms share the factor , we just add the coefficients: .

Understanding this problem

Learning Insight

Square roots of fractions follow the rule . Once you rationalize (remove square roots from denominators), the terms become like terms that can be combined just like variables.

Quick Tip

Spot as a common factor early. Once all terms are over the same denominator and share , you only need to add the whole-number coefficients.

Common Mistake

Students often add the fractions inside the square roots first — for example writing — but you CANNOT add under the radicals before taking the square roots separately.