Solve Square Root Expression: √2 × √2 × √0 Multiplication Problem

Q: Why does multiplying by zero always give zero?

The Zero Property of Multiplication states that any number times zero equals zero. Think of it as having zero groups of something - you end up with nothing!

Q: What is the square root of zero?

$ \sqrt{0} = 0 $ because 0 × 0 = 0. Zero is the only number that equals its own square root!

Q: Do I need to calculate the other square roots first?

No! Once you see $ \sqrt{0} $ in a multiplication, you know the answer is zero immediately. This saves time and prevents calculation errors.

Q: Would this work with cube roots or other roots of zero?

Yes! $ \sqrt[3]{0} = 0 $, $ \sqrt[4]{0} = 0 $, etc. Any root of zero is zero, so the zero property applies to all root expressions.

Q: What if the problem had addition instead of multiplication?

With addition like $ \sqrt{2} + \sqrt{2} + \sqrt{0} $, you'd get $ 2 + 2 + 0 = 4 $. The zero property only applies to multiplication, not addition!

Square Root Multiplication with Zero Property

Solve the following exercise:

$\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{0}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's simplify this expression together.

00:12 The square root of A, times the square root of B.

00:15 Is the same as the square root of A times B.

00:19 Now, let's use this formula to find a single square root.

00:24 First, calculate the product of the numbers.

00:29 And that's our solution! Well done.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{0}=$

Step-by-step solution

Notice that in the given problem, a multiplication is performed between three terms, one of which is:

$\sqrt{0}$ and let's remember that the root (of any order) of the number 0 is 0, meaning that:

$\sqrt{0}=0$ and since multiplying any number by 0 will always yield the result 0,

therefore the result of the multiplication in the problem is 0, meaning:

$\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{0}=\\ \sqrt{2}\cdot\sqrt{2}\cdot0=\\ \boxed{0}$ and thus the correct answer is answer C.

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero always equals zero
Root Property: $\sqrt{0} = 0$ since 0 × 0 = 0
Check: $\sqrt{2} \cdot \sqrt{2} \cdot 0 = 2 \cdot 0 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring the zero term and multiplying only the square roots
Don't solve $\sqrt{2} \cdot \sqrt{2} = 2$ and ignore the zero = wrong answer 2! The zero factor makes the entire product zero regardless of other terms. Always recognize that any multiplication involving zero equals zero.

Practice Quiz

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Choose the largest value

FAQ

Everything you need to know about this question

Why does multiplying by zero always give zero?

The Zero Property of Multiplication states that any number times zero equals zero. Think of it as having zero groups of something - you end up with nothing!

What is the square root of zero?

$\sqrt{0} = 0$ because 0 × 0 = 0. Zero is the only number that equals its own square root!

Do I need to calculate the other square roots first?

No! Once you see $\sqrt{0}$ in a multiplication, you know the answer is zero immediately. This saves time and prevents calculation errors.

Would this work with cube roots or other roots of zero?

Yes! $\sqrt[3]{0} = 0$ , $\sqrt[4]{0} = 0$ , etc. Any root of zero is zero, so the zero property applies to all root expressions.

What if the problem had addition instead of multiplication?

With addition like $\sqrt{2} + \sqrt{2} + \sqrt{0}$ , you'd get $2 + 2 + 0 = 4$ . The zero property only applies to multiplication, not addition!

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Solve Square Root Expression: √2 × √2 × √0 Multiplication Problem

Square Root Multiplication with Zero Property

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does multiplying by zero always give zero?

What is the square root of zero?

Do I need to calculate the other square roots first?

Would this work with cube roots or other roots of zero?

What if the problem had addition instead of multiplication?

🌟 Unlock Your Math Potential

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