Multiply Square Roots: Solving √5 × √5

Solve the following exercise:

55= \sqrt{5}\cdot\sqrt{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem together.
00:09 When you multiply the square root of one number by the square root of another,
00:14 you get the square root of the product of these numbers.
00:18 Let's apply this formula to our exercise.
00:22 First, calculate the product of the numbers.
00:26 And that's how you find the solution!

Step-by-step written solution

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1

Understand the problem

Solve the following exercise:

55= \sqrt{5}\cdot\sqrt{5}=

2

Step-by-step solution

In order to simplify the given expression, we will use two laws of exponents:

a. The definition of root as an exponent:

an=a1n \sqrt[n]{a}=a^{\frac{1}{n}} b. The law of exponents for multiplication between terms with identical bases:

aman=am+n a^m\cdot a^n=a^{m+n}

Let's start by converting the square roots to exponents using the law mentioned in a:

55=512512= \sqrt{5}\cdot\sqrt{5}= \\ \downarrow\\ 5^{\frac{1}{2}}\cdot5^{\frac{1}{2}}= We'll continue, since we are multiplying two terms with identical bases - we'll use the law of exponents mentioned in b:

512512=512+12=51=5 5^{\frac{1}{2}}\cdot5^{\frac{1}{2}}= \\ 5^{\frac{1}{2}+\frac{1}{2}}=\\ 5^1=\\ \boxed{5} Therefore, the correct answer is answer a.

3

Final Answer

5 5

Practice Quiz

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Solve the following exercise:

\( \sqrt{\frac{2}{4}}= \)

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