Question

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.

2 square root of 12
2 square root of 2
6 square root of 5 end root minus 4 square root of 7
6 square root of 10 end root minus 4 square root of 14

Answer 1

Simplify √ 45 to 3√ 5 and √ 28 to 2√ 7

Which gives you (3√5 +3√ 5 )+(−2√ 7 −2√ 7 )

Combine like terms = 6√ 5 −4√ 7

So the answer would be

6 square root of 5 end root minus 4 square root of 7

Answer 2

Hence, the simplified expression is:

6 square root of 5 end root minus 4 square root of 7.

i.e.
`6√(5)-4√(7)`

Explanation:

We are asked to simplify the expression:

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.

which mathematically is given by:

`3√(5)-2√(7)+√(45)-√(28)`

Since, we know that:

`\sqrt[45}=√(3* 3* 5)\\\\i.e.\\\\√(45)=3√(5)`

and

`√(28)=√(2* 2* 7)\\\\i.e.\\\\√(28)=2√(7)`

i.e. we need to simplify:

`3√(5)-2√(7)+3√(5)-2√(7)`

Now, we combine the like terms as follows:

`=3√(5)+3√(5)-2√(7)-2√(7)\\\\=6√(5)-4√(7)`