Solve: Square Root of 4/2 Plus Square Root of 6/3

Question

Solve the following exercise:

42+63= \sqrt{\frac{4}{2}}+\sqrt{\frac{6}{3}}=

Video Solution

Solution Steps

00:00 Solve the following problem
00:03 Calculate each fraction
00:12 Every root is essentially itself multiplied by 1
00:24 It seems they have a common denominator, let's proceed to collect terms
00:27 This is the solution

Step-by-Step Solution

To solve this problem, we'll eliminate fractions under the square roots by simplifying directly:

  • Step 1: Simplify each fraction inside the square roots:
    42=2 \frac{4}{2} = 2 and 63=2 \frac{6}{3} = 2 .
  • Step 2: Apply the square root to each simplified fraction:
    42=2\sqrt{\frac{4}{2}} = \sqrt{2} and 63=2\sqrt{\frac{6}{3}} = \sqrt{2}.
  • Step 3: Add the results of the square roots:
    2+2=22\sqrt{2} + \sqrt{2} = 2\sqrt{2}.

Therefore, the solution to the problem is 222\sqrt{2}.

Answer

22 2\sqrt{2}