Solve the Square Root Product: √1 × √2 Step-by-Step

Solve the following exercise:

1⋅2= \sqrt{1}\cdot\sqrt{2}=

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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.
00:10 Imagine the square root of a number A, times the square root of another number B.
00:16 This equals the square root of the product, A times B.
00:21 Now, let's use this formula in our exercise and calculate the product.
00:26 That's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

1⋅2= \sqrt{1}\cdot\sqrt{2}=

2

Step-by-step solution

Let's start by recalling how to define a square root as a power:

an=a1n \sqrt[n]{a}=a^{\frac{1}{n}}

Next, we remember that raising 1 to any power always gives us 1, even the half power we got from converting the square root.

In other words:

1⋅2=↓12⋅2=112⋅2=1⋅2=2 \sqrt{1} \cdot \sqrt{2}= \\ \downarrow\\ \sqrt[2]{1}\cdot \sqrt{2}=\\ 1^{\frac{1}{2}} \cdot\sqrt{2} =\\ 1\cdot\sqrt{2}=\\ \boxed{\sqrt{2}} Therefore, the correct answer is answer a.

3

Final Answer

2 \sqrt{2}

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

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

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