Question

Please Help!
Simplify the radical expression.
2sqrt*7+5sqrt*28.

Answer 1

\[ 2 \sqrt{7} +5 \sqrt{28} \]
you should factor the 28, and look for *pairs* of numbers
remember that \( \sqrt{x\cdot x} \) simplifies to x
example: \( \sqrt{4} = \sqrt{2\cdot 2}\) and we can simplify the square root of 2*2 to just 2
\( \sqrt{4} = \sqrt{2\cdot 2} =2\)

example 2:
\[ \sqrt{12} = \sqrt{2\cdot 2 \cdot 3} = \sqrt{2\cdot 2} \sqrt{3}= 2 \sqrt{3}\]

Answer 2

can you find the factors of 28 ? are there any pairs ?

Answer 3

4 and 7

Answer 4

I actually got the answer 11sqrt7 for that problem. I asked for help on the wrong problem.. the problem I need help with is sqrt50-sqrt18-3sqrt12.

Answer 5

\[2\sqrt{7}+5\sqrt{28}\]\[2\sqrt{7}+5\sqrt{7 \times 4}\]\[2\sqrt{7}+(5\sqrt{7} \times \sqrt{4})\]\[2\sqrt{7}+(5\sqrt{7} \times 2)\]\[2\sqrt{7}+10\sqrt{7}= 12\sqrt {7} \]

Answer 6

dangit! I had it wrong?! lol Thank you!

Answer 7

Ok. So I have 50sqrt2. 9sqrt2? Is this right?

Answer 8

\[\sqrt{50}-\sqrt{18}-3\sqrt{12}\]\[5\sqrt{2}-3\sqrt{2}-(3 \times 2)\sqrt{2}\]\[5\sqrt{2}-3\sqrt{2}-6\sqrt{2}\]\[(5-3-6)\sqrt{2}\]\[-4\sqrt{2}\]

Answer 9

see how I am taking the perfect squares out of the square roots?

Answer 10

what is your actual question, I keep misunderstanding you, sorry.

Answer 11

The answer in the book is 2sqrt2-6sqrt3.. I understand how you are taking the perfect squares out though. Simplify the radical expressions. sqrt*50-sqrt*18-3sqrt*12

Answer 12

I did your question above then, but the book is wrong.

Answer 13

Either I misread the question, or you mis-wrote it, or the book is stupid.

Answer 14

***
the problem I need help with is sqrt50-sqrt18-3sqrt12.
Ok. So I have 50sqrt2. 9sqrt2? Is this right?
***
\[ \sqrt{50} - \sqrt{18} - 3 \sqrt{12} \]

each square root, one at at time:
50 factors into 2*25 = 2*5*5 <-- notice the pair of 5's.
18 = 2*9= 2*3*3 <-- Look! a pair of 3's
12= 2*6= 2*2*3 <--- a pair of twos.

We can take a pair out of the square root, toss one of the pair, and put the remaining number "out front"
For example: \( \sqrt{50} = \sqrt{2\cdot 5 \cdot 5} = 5 \sqrt{2} \)
do that to the other square roots:
\[ \sqrt{18} = \sqrt{2 \cdot 3 \cdot 3} = 3 \sqrt{2} \\
\sqrt{12} = \sqrt{2 \cdot 2 \cdot 3} =2 \sqrt{3} \]
the original problem is now
\[ \sqrt{50} - \sqrt{18} - 3 \sqrt{12} \\ 5 \sqrt{2}-3 \sqrt{2} +-3 \cdot 2 \sqrt{3}
\]
notice that you have 5 square roots of 2 take away 3 square roots of 2, leaving 2 square roots of 2 or \( 2 \sqrt{2} \)
also -3*2 = -6 in front of the sqrt of 3.
The final answer is
\[ 2 \sqrt{2} -6 \sqrt{3} \]