Solve Square Root Multiplication: √16 × √1 Step-by-Step

Q: Why can't I just add 16 + 1 under one square root?

Because $ \sqrt{16} \times \sqrt{1} $ is multiplication, not addition! The property $ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} $ means you multiply the numbers inside: $ \sqrt{16 \times 1} = \sqrt{16} $.

Q: What is a perfect square and why does it matter?

A perfect square is a number that equals some integer squared, like 16 = 4². Perfect squares have whole number square roots, making calculations much easier!

Q: Do I always need to simplify square roots first?

Yes! Always simplify square roots of perfect squares immediately. $ \sqrt{16} = 4 $ and $ \sqrt{1} = 1 $ make the multiplication much clearer.

Q: What if one of the square roots wasn't a perfect square?

You can still use the property $ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} $. For example: $ \sqrt{16} \times \sqrt{2} = 4\sqrt{2} $ or $ \sqrt{32} $.

Q: Why does √1 always equal 1?

Because 1 × 1 = 1, so the square root of 1 is 1. In fact, any power of 1 always equals 1, including fractional powers like $ 1^{1/2} $!

Square Root Multiplication with Perfect Squares

Solve the following exercise:

$\sqrt{16}\cdot\sqrt{1}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together!

00:10 We know that the square root of A, times the square root of B, is the square root of A times B.

00:17 Now, apply this rule to our exercise, and we'll calculate their product.

00:22 First, let's find the square root of sixteen.

00:26 Sixteen's square root is four. That's the answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\sqrt{16}\cdot\sqrt{1}=$

Step-by-step solution

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

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

Next, we will remember that raising 1 to any power will always yield the result 1, even the half power of the square root.

In other words:

$\sqrt{16}\cdot\sqrt{1}= \\ \downarrow\\ \sqrt{16}\cdot\sqrt[2]{1}=\\ \sqrt{16}\cdot 1^{\frac{1}{2}}=\\ \sqrt{16} \cdot1=\\ \sqrt{16} =\\ \boxed{4}$ Therefore, the correct answer is answer D.

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Square roots of perfect squares simplify to whole numbers
Technique: Calculate $\sqrt{16} = 4$ and $\sqrt{1} = 1$ first
Check: Verify that 4 × 1 = 4 matches final answer ✓

Common Mistakes

Avoid these frequent errors

Adding under the square root instead of multiplying separately
Don't write $\sqrt{16 + 1} = \sqrt{17}$ = wrong result! Square root multiplication doesn't work like addition under one radical. Always multiply the simplified square roots: $\sqrt{16} \times \sqrt{1} = 4 \times 1 = 4$ .

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

FAQ

Everything you need to know about this question

Why can't I just add 16 + 1 under one square root?

Because $\sqrt{16} \times \sqrt{1}$ is multiplication, not addition! The property $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ means you multiply the numbers inside: $\sqrt{16 \times 1} = \sqrt{16}$ .

What is a perfect square and why does it matter?

A perfect square is a number that equals some integer squared, like 16 = 4². Perfect squares have whole number square roots, making calculations much easier!

Do I always need to simplify square roots first?

Yes! Always simplify square roots of perfect squares immediately. $\sqrt{16} = 4$ and $\sqrt{1} = 1$ make the multiplication much clearer.

What if one of the square roots wasn't a perfect square?

You can still use the property $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ . For example: $\sqrt{16} \times \sqrt{2} = 4\sqrt{2}$ or $\sqrt{32}$ .

Why does √1 always equal 1?

Because 1 × 1 = 1, so the square root of 1 is 1. In fact, any power of 1 always equals 1, including fractional powers like $1^{1/2}$ !

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Solve Square Root Multiplication: √16 × √1 Step-by-Step

Square Root Multiplication with Perfect Squares

❤️ 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 can't I just add 16 + 1 under one square root?

What is a perfect square and why does it matter?

Do I always need to simplify square roots first?

What if one of the square roots wasn't a perfect square?

Why does √1 always equal 1?

🌟 Unlock Your Math Potential

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