Question

Simplify √28 . √27 . √5

Simplify 2√5 + 3√5 - √5

Which expression is equal to 2√28 - 5√63

A) -√7
B) -37√7
C) √7
D) -11√7

Thank you

Answer 1

1. 6√105

2. 4√5

3. D

Explanation:

Math is an interesting invention.

Answer 2

Simplify
`√(28) * √(27) * √(5)`

Observe that all roots are similar, because they are square roots.

To simplify this products, we can write only one root and multiply all sub-radical numbers, as follows

`√(28) * √(27) * √(5)=√(28 * 27 * 5)`

It's better to maintain the product as factors, so, let's express each number in a power

`√(28) * √(27) * √(5)=√(28 * 27 * 5)=\sqrt{2^(2) * 7 * 3^(2) * 3 * 5 }`

Then, all square powers can go out the root

`\sqrt{2^(2) * 7 * 3^(2) * 3 * 5 }=2* 3 √(105)=6 √(105)`

Therefore, the answer here is
`6√(105)`

Simplify
`2√(5)+3√(5)-√(5)`

Observe that all roots are exactly the same, we proceed to sum and subtract the whole part of each term

`2√(5)+3√(5)-√(5)=(2+3-1)√(5)=4√(5)`

Therefore, the answer is
`4√(5)`

Which expression is equal to
`2√(28)-5√(63)`

Let's express each root in factors

`2√(28)-5√(63)=2√(7 * 4) -5 √(7 * 9)`

Then, we solve the root for 4 and 9

`2√(7 * 4) -5 √(7 * 9)=4√(7)-15√(7)`

Then, we subtract

`4√(7)-15√(7)=-11√(7)`

Therefore, the right answer is D.