Solve √(36/144) × √√16: Multiple Square Root Operations

Video Solution

Solution Steps

00:00 Solve the following problem

00:03 The root of a fraction (A divided by B)

00:06 Equals the root of the numerator (A) divided by the root of the denominator (B)

00:10 We'll apply this formula to our exercise

00:20 Break down 36 to 6 squared

00:23 Break down 144 to 12 squared

00:27 Break down 16 to 4 squared

00:31 The root cancels the square

00:44 Break down 12 into factors of 6 and 2

00:48 Break down 4 into 2 squared

00:52 Simplify wherever possible

00:55 The root cancels the square

01:00 This is the solution

Step-by-Step Solution

To solve the expression $\sqrt{\frac{36}{144}} \cdot \sqrt{\sqrt{16}}$ , follow these steps:

Simplify $\sqrt{\frac{36}{144}}$ :
- Evaluate the fraction: $\frac{36}{144} = \frac{1}{4}$ .
- Take the square root: $\sqrt{\frac{1}{4}} = \frac{1}{2}$ because $\sqrt{1} = 1$ and $\sqrt{4} = 2$ .
Simplify $\sqrt{\sqrt{16}}$ :
- First evaluate the inner square root: $\sqrt{16} = 4$ since $4^2 = 16$ .
- Then take the square root of the result: $\sqrt{4} = 2$ since $2^2 = 4$ .
Multiply the results from both parts:
- Multiply the simplified results: $\frac{1}{2} \cdot 2 = 1$ .

Therefore, the solution to the expression is $1$ .