What is #4sqrt42 + 2sqrt28 - sqrt7#?

Question

Mila Anderson · Accepted Answer

#=sqrt7(4sqrt6+1)#

Write each of the radicands as a product of the factors:

#4sqrt42+2sqrt28-sqrt7#

#=4sqrt(6xx7) +2sqrt(4xx7) -sqrt7#

Split the roots into separate roots.

#=4sqrt6sqrt7 +sqrt4 sqrt7-sqrt7#

#=4sqrt6sqrt7 + 2sqrt7-sqrt7#

Take out the common factor of #sqrt7# from each term

#=sqrt7(4sqrt6 +2-1)#

#=sqrt7(4sqrt6+1)#

You cannot simplify further without a calculator.

Jeremiah Andrews · Answer

undefined To simplify the expression $ 4\sqrt{42} + 2\sqrt{28} - \sqrt{7} $:

1. First, simplify the square roots where possible:
   - $ \sqrt{42} = \sqrt{2 \times 21} = \sqrt{2} \times \sqrt{21} $
   - $ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7} $

2. Substitute the simplified square roots back into the expression:
   $ 4\sqrt{42} + 2\sqrt{28} - \sqrt{7} = 4\sqrt{2} \times \sqrt{21} + 2(2\sqrt{7}) - \sqrt{7} $

3. Combine like terms:
   $ 4\sqrt{2} \times \sqrt{21} + 2(2\sqrt{7}) - \sqrt{7} = 4\sqrt{2} \times \sqrt{21} + 4\sqrt{7} - \sqrt{7} $

4. Simplify further:
   $ 4\sqrt{2} \times \sqrt{21} + 4\sqrt{7} - \sqrt{7} = 4\sqrt{42} + 3\sqrt{7} $

So, $ 4\sqrt{42} + 2\sqrt{28} - \sqrt{7} $ simplifies to $ 4\sqrt{42} + 3\sqrt{7} $.