Simplify the Radical Expression: √10/√2 Step-by-Step

Question

Solve the following exercise:

102= \frac{\sqrt{10}}{\sqrt{2}}=

Video Solution

Solution Steps

00:00 Solve the following problem
00:03 Break down 10 into factors of 5 and 2
00:09 When we have a root of the multiplied terms (A times B)
00:13 We can convert it to the multiplication of the root(A²) times the root(B)
00:17 Apply this formula to our exercise and proceed to convert to 2 roots:
00:26 Simplify wherever possible
00:29 This is the solution

Step-by-Step Solution

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

  • Step 1: Apply the square root quotient property.
  • Step 2: Simplify the fraction under the square root.
  • Step 3: Evaluate the square root if possible.

Now, let's work through each step:
Step 1: The square root quotient property tells us that 102=102\frac{\sqrt{10}}{\sqrt{2}} = \sqrt{\frac{10}{2}}.
Step 2: Simplify the fraction inside the square root: 102=5\frac{10}{2} = 5.
Step 3: Therefore, 102=5\sqrt{\frac{10}{2}} = \sqrt{5}.

Therefore, the solution to the problem is 5 \sqrt{5} .

Answer

5 \sqrt{5}