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Chapter 5: Problem 90

Explain how to add square roots with the same radicand.

Short Answer

Expert verified
To add square roots with the same radicand, treat them like algebraic like terms. For example, \(3\sqrt{2} + 2\sqrt{2}\) would result in \(5\sqrt{2}\). However, remember that if the radicands are different, they can't be directly added together.

Step by step solution

01

Understand the Term Radicand

A radicand refers to the number under a square root. For example, in the square root of 2, '2' is the radicand. Only square roots with the same radicands can be added together directly.
02

Add Like Terms

When you have expressions with the same radicand such as 3\(\sqrt{2}\) and 2\(\sqrt{2}\), treat them as algebraic like terms, much like you would treat \(3x\) and \(2x\) as like terms in algebraic addition. So 3\(\sqrt{2}\) + 2\(\sqrt{2}\) becomes \(5\sqrt{2}\).
03

Handle Different Radicands

If the radicands are different, for example \(\sqrt{2}\) and \(\sqrt{3}\), they cannot be added directly using simple addition. These are treated as distinct and separate terms, much like \(x\) and \(y\) in algebra.

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Most popular questions from this chapter

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

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