Solve Square Root Multiplication: √1 × √25

Question

Solve the following exercise:

125= \sqrt{1}\cdot\sqrt{25}=

Video Solution

Solution Steps

00:07 Let's solve this problem step by step.
00:10 The square root of A times the square root of B equals the square root of A times B.
00:17 We'll apply this formula to our problem and find the answer.
00:22 Break down 25 as 5 to the power of 2.
00:26 Taking the square root of 5 squared just gives us 5.
00:31 And that's the solution! Great job!

Step-by-Step Solution

To solve the expression 125 \sqrt{1} \cdot \sqrt{25} , we will use the Product Property of Square Roots.

According to the property, we have:

125=125\sqrt{1} \cdot \sqrt{25} = \sqrt{1 \cdot 25}

First, calculate the product inside the square root:

125=251 \cdot 25 = 25

Now the expression simplifies to:

25\sqrt{25}

Finding the square root of 25 gives us:

55

Thus, the value of 125 \sqrt{1} \cdot \sqrt{25} is 5\boxed{5}.

After comparing this solution with the provided choices, we see that the correct answer is choice 3.

Answer

5 5