Simplify the Square Root: √(196/49) Step-by-Step Solution

Complete the following exercise:

19649= \sqrt{\frac{196}{49}}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:03 The root of the fraction (A divided by B)
00:07 Equals the root of the numerator (A) divided by the root of the denominator (B)
00:11 Apply this formula to our exercise
00:19 Factorize 196 into 14 squared
00:24 Factorize 19 into 7 squared
00:29 The root of any number (A) squared cancels out the square
00:32 Apply this formula to our exercise and proceed to cancel out the squares
00:41 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

19649= \sqrt{\frac{196}{49}}=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Apply the square root quotient property.
  • Step 2: Calculate the square roots of the numerator and the denominator.
  • Step 3: Simplify the resulting expression.

Now, let's work through each step:
Step 1: Apply the square root quotient property 19649=19649 \sqrt{\frac{196}{49}} = \frac{\sqrt{196}}{\sqrt{49}} .
Step 2: Calculate the individual square roots: 196=14 \sqrt{196} = 14 and 49=7 \sqrt{49} = 7 .
Step 3: Simplify the expression to 147=2 \frac{14}{7} = 2 .

Therefore, the solution to the problem is 2.

3

Final Answer

2

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that is equal to the following:

\( \sqrt{a}:\sqrt{b} \)

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