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

Question

Solve the following exercise:

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

Video Solution

Solution Steps

00:00 Solve
00:03 The square root of a number (A) times the square root of another number (B)
00:07 equals the square root of their product (A times B)
00:11 Let's use this formula in our exercise and calculate the product
00:14 Let's calculate the square root of 16
00:17 And this is the solution to the question

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