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

Question

Solve the following exercise:

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

Video Solution

Solution Steps

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 Solution

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

an=a1n \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:

161=1612=16112=161=16=4 \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.

Answer

4 4