Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus square root of 45 end root minus square root of 28.
A.2 square root of 12
B.2 square root of 2
C.6 square root of 5 - 4 square root of7
D.6 square root of 10 - 4 square root of 14
3√5 - 2√7 + √45 - √28
since 45=9*5 and 28=4*7, that is
= 3√5 - 2√7 + 3√5 - 2√7
= 6√5 - 4√7
Well, isn't that a tangled mess of square roots! Let's see if we can untangle it together.
First, let's simplify each square root separately. The square root of 5 end root can't be simplified any further. However, the square root of 45 end root can be simplified to 3 square root of 5 end root. And the square root of 28 can be simplified to 2 square root of 7 end root.
So now our expression looks like this: 3 square root of 5 end root minus 2 square root of 7 end root plus 3 square root of 5 end root minus 2 square root of 7 end root.
Now, let's collect like terms. We have 3 square root of 5 end root plus 3 square root of 5 end root, which equals 6 square root of 5 end root. And we have minus 2 square root of 7 end root minus 2 square root of 7 end root, which equals minus 4 square root of 7 end root.
Putting it all together, our simplified expression is 6 square root of 5 end root minus 4 square root of 7 end root. And that matches option C: 6 square root of 5 - 4 square root of 7.
So, the final answer is option C: 6 square root of 5 - 4 square root of 7.
To simplify the expression, we need to simplify each square root separately.
Square root of 5 can't be simplified further, so it remains as square root of 5.
Square root of 7 can't be simplified further, so it remains as square root of 7.
Next, let's simplify the square roots of 45 and 28.
The prime factorization of 45 is 3 * 3 * 5. We can take out one factor of 3 from the square root and simplify it as 3 square root of 5.
The prime factorization of 28 is 2 * 2 * 7. We can take out one factor of 2 from the square root and simplify it as 2 square root of 7.
Now let's substitute these simplified square roots back into the original expression:
3 square root of 5 - 2 square root of 7 + 3 square root of 5 - 2 square root of 7
Combining like terms:
(3 square root of 5 + 3 square root of 5) - (2 square root of 7 + 2 square root of 7)
Simplifying further:
6 square root of 5 - 4 square root of 7
Therefore, the simplified form of the expression is C. 6 square root of 5 - 4 square root of 7.
To simplify the given expression, you can start by simplifying each square root term individually.
Step 1: Simplify the square root terms
Square root of 5 = √5
Square root of 7 = √7
Square root of 45 = √(9 * 5) = √9 * √5 = 3√5
Square root of 28 = √(4 * 7) = √4 * √7 = 2√7
Now substitute the simplified square root terms back into the original expression:
3√5 - 2√7 + 3√5 - 2√7
Step 2: Combine like terms
Combine the square root terms with the same radicands (the numbers inside the square roots):
(3√5 + 3√5) - (2√7 + 2√7)
= 6√5 - 4√7
Therefore, the simplified form of 3√5 - 2√7 + √45 - √28 is 6√5 - 4√7.
Therefore, the correct answer is option C: 6√5 - 4√7.